Physics-Informed ML

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60 papers in the last four weeks, up 131% on the four weeks before. 0.6% of all new papers.

Jul 13Week of Sep 28

Latest papers 561

Jun 15, 2026cs.CL

Progressive Knowledge-Guided Large Language Model Framework for Bearing Fault Diagnosis

Vibration-based bearing fault diagnosis requires resolving three interrelated measurement challenges, including the trade-off between global statistical feature efficiency and local transient signal fidelity, insufficient traceability of measurement features to underlying fault physics, and ineffective multi-source measurement information fusion across diagnostic scales. This paper presents a progressive physics-guided multi-scale vibration signal processing framework that addresses all three challenges within a unified diagnostic pipeline. An 81-dimensional measurement descriptor, derived from bearing kinematic theory and characteristic defect frequencies, establishes a physically traceable feature space enabling real-time fault screening at approximately 20 ms per sample. A fault-adaptive signal segmentation mechanism then directs analytical attention toward fault-relevant waveform regions guided by physics-based priors, without manual feature engineering. Structured fault mechanism knowledge is further encoded implicitly in model parameters during training, enabling autonomous multi-scale measurement fusion without external knowledge dependencies at inference. Validated on four public benchmark datasets under diverse operating conditions, the framework achieves 98.49% diagnostic accuracy with a 12.6-fold reduction in computational cost relative to signal-level baselines. Interpretability analysis confirms that diagnostic feature activations align with established bearing fault mechanics, supporting measurement traceability in safety-critical industrial systems.

Jinghan Wang, Gaoliang Peng, Yanjun Chen +3

Harbin Institute of Technology, China · Eastern Institute of Technology, China

Multi-Scale Feature Fusion Physics-Informed ML Bearing Fault Diagnosis

Jun 15, 2026math.NA

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.

Vijay Kumar, Gautam Singh

Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, 620015, Tamil Nadu, India.

Neural PDE Solvers Physics-Informed ML

Jun 15, 2026cs.CV

Beer-Lambert Guided Representation Learning for Unsupervised Anomaly Detection in Sub-THz Food Inspection Images

Food manufacturing requires reliable inspection systems to detect foreign material contamination and maintain product safety. Sub-THz transmission imaging provides material-dependent attenuation characteristics that are useful for detecting low-density contaminants in food products. However, existing unsupervised anomaly detection methods mainly rely on RGB-pretrained visual representations, which may not adequately capture the transmission behavior of Sub-THz images. This paper proposes a Beer-Lambert guided representation learning framework for unsupervised anomaly detection in Sub-THz food inspection images. The proposed method introduces an attenuation decomposition module as an auxiliary regularization module that constrains student representations through attenuation reconstruction during training. In addition to the conventional one-class setting, we introduce a Leave-One-Food-Out protocol to evaluate generalization capability under unseen food categories. Experimental results on the Inline-Food-Inspection-THz dataset show that the proposed method improves overall anomaly detection performance over the baseline method.

Gyutae Hwang, Sang Jun Lee

Division of Electronics and Information Engineering, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju, 54896, Jeonbuk-do, Republic of Korea

Industrial Anomaly Detection Industrial Inspection Unsupervised Anomaly Detection Physics-Informed ML

Jun 15, 2026cs.LG

SciML in the Wild: A Diagnostic Study of When Structural Priors Help and When They Hurt

Scientific Machine Learning (SciML) methods such as Neural Ordinary Differential Equations (NODEs), Physics-Informed Neural Networks (PINNs), and Universal Differential Equations (UDEs) are most effective when structural priors reflect reliable governing dynamics. We ask what happens when this assumption is violated. Using macroeconomic forecasting as a stress-test domain, we evaluate five model families, ARIMA, LSTM, NODE, PINN, and UDE, across 23 countries using sparse annual data, multiple temporal splits, and five random seeds. Our results show that none of the evaluated models achieve consistently strong forecasting performance, highlighting the difficulty of low-frequency macroeconomic prediction. However, a clear relative hierarchy emerges: less-constrained models, particularly ARIMA and NODE, consistently outperform more-constrained heuristic-prior models such as PINN and UDE. Rather than treating this as a rejection of SciML, we interpret it as a diagnostic result: structural priors can act as misregularizers when they do not match the data-generating process. We identify failure modes including prior misalignment, regime shifts, structural breaks, and optimization instability, and argue that SciML practitioners should test whether structure helps before assuming that more structure is beneficial.

Vrishank Sai Anand, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar +2

GEMS Modern Academy Dubai, United Arab Emirates · Vizuara AI Labs, Pune, India

Time Series Forecasting Scientific ML Physics-Informed ML Neural ODEs

Jun 15, 2026cs.LG

Phys-JEPA: Physics-Informed Latent World Models for Multivariate Time-Series Forecasting

Multivariate forecasting in physical systems requires models that predict coupled temporal variables while preserving meaningful state evolution. Deep forecasters can fit temporal correlations, and physics-informed models can regularize predictions with scientific constraints, but these directions are often connected only at the decoded-output level. As a result, the hidden predictive state that generates future trajectories may remain statistically useful but physically unstructured. We introduce Phys-JEPA, a physics-informed joint-embedding predictive architecture for multivariate time-series forecasting. Phys-JEPA learns a latent world model in which predictive states are decomposed into physical and residual components, and physical consistency is imposed directly on latent states and latent transitions rather than only on decoded forecasts. This formulation uses known physical variables to organize the representation space while retaining residual capacity for unresolved dynamics. On Jena Climate 2009--2016, Phys-JEPA reduces aggregate MSE from 0.12482 to 0.12273 and temperature MSE from 0.01892 to 0.01831 at H=24. On Traffic, full Phys-JEPA improves aggregate MSE over the supervised baseline across all tested horizons, reducing H=192 MSE from 0.800784 to 0.773873. On Electricity, the best variant depends on horizon: static latent consistency is strongest at H=24 and H=48, while full Phys-JEPA gives the best aggregate and target-variable MSE at H=192. These initial results suggest that moving physics-informed learning from output space to latent predictive state space is a promising direction for interpretable temporal world models.

Weizhi Nie, Weichao Liu, Honglin Guo +1

Tianjin University

Multivariate Time Series Forecasting Latent Dynamics Modeling Joint-Embedding Predictive Architecture Physics-Informed ML

Jun 14, 2026cs.LG

HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology

A digital twin (DT) of a patient-specific heart offers significant potential in personalized medicine. However, its rapid and dynamic adaptation to an individual's live data and its predictive capability after adaptation remains central challenges. We examine this challenge from its two building blocks: DT formulation where mechanistic and data-driven models show competing merits and limitations, and DT optimization strategies that are largely driven by a reconstruction objective leading to un-identifiable models. We address both bottlenecks via HAPI -- an AI framework for building hybrid, adaptive, and predictive DTs with three key enablers. First, HAPI constructs a physics-integrated gray-box model in which an interpretable mechanistic backbone is augmented by a neural component that models its residual to the observed data. Second, rather than attempting to pre-encode all possible variations in a static hybrid model, HAPI enables rapid on-the-fly adaptation of the hybrid model to few-shot live data, achieved by feedforward meta-learners realizing amortized inference of both mechanistic and neural parameters of the hybrid model trained with predictive objectives. Finally, we show that this adaptivity corresponds to the construction of a conditional generative model (i.e., the hybrid DT) that endows it with theoretical identifiability and thus strong performance in predictive scenarios. We demonstrate the proof-of-concept of HAPI in cardiac electrophysiology using a hybrid monodomain model with mechanistic reaction kinetics and neural graph diffusion. Across synthetic and real-data studies, we show that HAPI's mechanistic-neural hybridization and predictive adaptation are critical for obtaining identifiable DTs with strong predictive and out-of-distribution capabilities.

Sumeet Vadhavkar, Xiajun Jiang, Yubo Ye +2

Adaptive Inference Physics-Informed ML Digital Twins

Jun 13, 2026math.OC

Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper System

This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system. The classical linear-quadratic optimal control problem is solved by two independent classical methods -- Pontryagin's Minimum Principle with single shooting, and direct transcription through trapezoidal collocation -- and recast as a constrained optimization problem solved by two feedforward neural networks: a state network whose boundary conditions are enforced exactly through a composite cubic-and-mask ansatz, and an unconstrained control network. The composite loss combines the physics residual at the collocation points with a trapezoidal approximation of the cost functional, weighted by a single scalar hyperparameter. On the benchmark considered, the PINN reproduces the classical optimal cost to four significant digits, satisfies the terminal state constraints exactly by construction, and produces pointwise state and control errors that fall within the spread of the two classical references. Training is approximately two orders of magnitude slower than classical shooting on this benchmark, which is honestly reported. The contribution is methodological clarity rather than methodological novelty: the formulation and the accompanying Google Colab implementation are intended to lower the barrier to entry for practitioners exploring PINN-based optimal control without prior exposure to adjoint methods or two-point boundary value problems.

Abdeladhim Tahimi, Rinaldo Vieira da Silva Junior

Centro de Engenharias e Ciˆencias Agr´arias, Universidade Federal de Alagoas, Brazil

Physics-Informed ML Optimal Control

Jun 13, 2026cs.CV

Physics-Driven Zero-Shot MRI Reconstruction with Non-local Image Priors

Zero-Shot Self-Supervised Learning (ZS-SSL) has emerged as a promising paradigm for accelerated Magnetic Resonance Imaging (MRI) reconstruction, eliminating the reliance on fully-sampled external datasets. However, learning solely from a single under-sampled scan suffers from supervision scarcity and optimization instability, often leading to overfitting or artifacts. To address these challenges, we propose a robust physics-driven ZS-SSL framework that synergizes physical consistency with image-domain non-local priors. Our method introduces three core innovations: (1) a Coil Sensitivity Map (CSM)-Guided Dynamic Repository, which stabilizes the training trajectory by filtering physically inconsistent artifacts based on coil sensitivity constraints; (2) a SPIRiT-based regularization, which enforces k-space self-consistency via a learned correlation kernel and stochastic masking; (3) a Non-Local Self-Similarity (NSS) Pixel Bank, which leverages the high-fidelity reference established by the former modules to explicitly mine non-local anatomical similarities, thereby augmenting supervision in the image domain. Extensive experiments on the FastMRI dataset demonstrate that our approach achieves state-of-the-art performance, particularly under high acceleration factors, effectively bridging the gap between zero-shot learning and supervised methods. The code is available at https://github.com/Zolento/NS-SSL.

Lingtong Zhang, Wenlei Li, Mu He +2

School of Information Science and Technology, University of Science and Technology of China, Hefei, China

Self-Supervised Learning Image Reconstruction Accelerated MRI Reconstruction Physics-Informed ML

Jun 13, 2026cs.LG

Physics-conforming Latent Twins

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

Matthias Chung, Yutong Bu, Deepanshu Verma

Department of Mathematics, Emory University, 400 Dowman Drive, Atlanta, 30322, GA, USA · School of Mathematical and Statistical Sciences, Clemson University, 220 Parkway Drive, Clemson, 29634, SC, USA

Neural Surrogate Modeling Surrogate Modeling Latent Dynamics Modeling PDE Surrogate Modeling Physics-Informed ML

Jun 12, 2026cs.LG

A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge. In this study, we propose a hybrid GNN--FEM framework for efficient and generalizable phase-field fracture modeling. While phase-field approaches provide a robust variational framework for simulating complex crack evolution, their high computational cost limits practical applications because they require solving coupled, nonlinear, and history-dependent systems within an incremental finite element procedure. To address this challenge, a graph neural network surrogate is integrated into the conventional staggered scheme, replacing the phase-field update at each load increment while retaining the FEM-based displacement solver to enforce mechanical equilibrium and boundary conditions. By preserving the incremental solution structure, the framework remains consistent with history-dependent fracture evolution without requiring the surrogate to approximate the full solution trajectory. This selective surrogate strategy emphasizes the identification of a physically meaningful and incrementally structured learning target, rather than relying on brute-force data generation to learn the full fracture process. The proposed framework achieves strong generalization across varying geometries, loading conditions, material properties, and discretizations through dimensionless feature design, a graph-based formulation on mesh-based domains, and a physics-informed loss derived from the governing phase-field equation. Numerical experiments demonstrate that the hybrid approach reduces computational cost while maintaining accuracy compared with conventional FEM, and exhibits robust predictive performance across diverse problem settings.

Hyeonbin Moon, Yongjin Choi, Seunghwa Ryu

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · KAIST InnoCORE PRISM-AI Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · Department of AX, College of AI, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea

Structural Mechanics PDE Surrogate Modeling Physics-Informed ML Computational Materials Science

Jun 12, 2026cs.LG

Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed framework for discovering yield functions from full-field displacement data and reaction force data, without stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration, rather than through direct stress-space supervision. The yield function is represented by a convex neural network that enforces convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases. The proposed framework is validated using finite element (FE) benchmark studies with von Mises, Hill 1948, and Yld2000-2d yield functions, assessing yield contour agreement, displacement-noise sensitivity, identifiability through plastically active stress states, epistemic uncertainty, and polynomial-surrogate deployment. This study provides a mechanics-constrained pathway for discovering anisotropic yield functions from displacement and force data while keeping the identified component within the structure of elastoplastic stress integration.

Hyeonbin Moon, Donghyuk Cho, Jecheon Yu +2

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · School of Engineering, Deakin University, 75 Pigdons Road, Waurn Ponds, Victoria, 3216, Australia · KAIST InnoCORE PRISM-AI Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea +1

Parameter Identifiability Physics-Informed ML Inverse Problems

Jun 12, 2026math.NA

Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincaré View, with Application to Fluid-Structure Interaction with Contact

Physics-informed neural networks (PINNs) are meshless and carry moving geometry and topology change through resampling of collocation points; the finite-element method (FEM) is the workhorse for boundary-fitted discretisations. Coupling the two across a shared interface promises the best of both, yet existing PINN-FEM schemes are validated only empirically. We put the coupling on a domain-decomposition footing: viewing each solver as a Steklov-Poincaré (trace-to-flux) operator, we transfer the classical Dirichlet-Neumann (DN) divergence diagnosis and its Robin-Neumann (RN) cure, including a closed-form, sweep-free interface impedance, and prove a PINN-specific contraction theorem: a trained network realises only a perturbed Steklov operator with a per-step training residual, and RN still contracts, with no shared-eigenbasis hypothesis, to a floor set by the achieved training loss. Because a PINN has no stiffness matrix, we introduce a Fourier-mode interface probe that recovers the network's resolvable Steklov eigenvalues to within 0.5% and doubles as a diagnostic of the network's spectral cap. The theory predicts measured PINN-FEM contraction rates to within 7% on 1D and 2D Poisson couplings, and a two-slab analogue of the large-added-mass regime shows RN's per-mode impedance matching winning decisively where tuned scalar relaxation saturates. We demonstrate the framework on a Stokes/rigid-disc problem with Alart-Curnier contact: the meshless PINN fluid absorbs the topology change at contact by collocation exclusion alone, no remeshing and no cut cells, and the static-equilibrium contact reaction matches the submerged weight to 0.4% under mesh refinement. We quantify remaining limitations: the warm-started PINN drifts off the Stokes manifold over long horizons, and matched FEM-FEM benchmarks attribute pre-impact squeeze-film signatures to PINN under-resolution.

Mikel Landajuela

Lawrence Livermore National Laboratory

PDE Solving Physics-Informed ML Finite Element Method Physics-Based Simulation

Jun 11, 2026eess.IV

Full-Self Diagnostics (FSD): Physics-Grounded Visual Biomarker Inference from Smartphone Video via Inverse Problems and Operator Learning

We present Full-Self Diagnostics (FSD), a unified mathematical framework for recovering latent physiological states from unconstrained 9-second facial videos captured by consumer smartphones. The approach integrates five mutually reinforcing components: (1) a physics-based forward model derived from the radiative transfer equation and chromophore absorption that maps camera observables to biomarker concentrations; (2) an information-theoretic observability theory proving that multi-channel visual signals (spectral, pulse, respiratory, micro-expression, and oculomotor) contain strictly increasing mutual information with physiological state; (3) a stable, Tikhonov-regularized inverse problem with domain-uniform identifiability guarantees; (4) an operator-learning formulation that enables generalization across devices, resolutions, and populations; and (5) a supervised learning procedure, interpretable as stochastic variational inference, that continuously refines the model from paired biosensor ground truth with performance improving proportionally to one over the square root of the number of paired observations. Empirical validation on 38812 real-world paired scans across 59 subjects demonstrates practical performance. Self-collected data from the lead author (glucose range 35-550 mg/dL) yields MARD of 29.86 percent with 97.57 percent of predictions in Clarke Error Grid Zones A+B and only 0.27 percent in the dangerous Zone E. A well-managed diabetic participant achieves MARD of 17 percent in the narrower 70-180 mg/dL band. These results confirm that consumer-grade facial video encodes sufficient structured information for clinically relevant, non-invasive biomarker inference under fully unconstrained conditions, with performance scaling predictably as more paired data becomes available.

Jonathan Thomas, Harsh Thaker

Algomash® (Algorithmic Mashup Inc.)

Physics-Informed ML Inverse Problems

Jun 11, 2026cs.LG

A fully GPU-based workflow for building physics emulators of hypersonic flows

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

Fabian Paischer, Dylan Rubini, Deniz A. Bezgin +6

ELLIS Unit, Institute for Machine Learning, JKU Linz · EMMI AI, Linz · Chair of Aerodynamics and Fluid Mechanics, TU Munich, Germany

Neural Surrogate Modeling Physics-Informed ML Iterative Refinement Computational Fluid Dynamics

Jun 11, 2026cs.AI

Physics-Guided Spatiotemporal Learning for Coastal Wave Peak Period Estimation from Video

Wave parameters in the nearshore are crucial for coastal engineering, shoreline protection, marine hazard assessment, and coastal management for climate resilience. Traditional monitoring systems like buoys and radar platforms offer accurate monitoring but can have high installation and maintenance expenses and limited spatial coverage. Passive ocean monitoring using video has been achieved by leveraging deep learning, however, many methods are not physically interpretable, feasible, and validated for oceanography. In thiswork, a Physics-Guided Deep Spatiotemporal Learning Framework for direct estimation of nearshore wave peak periods from passive coastal video stream is proposed. The framework combines automated temporal-variance based region-of-interest detection, multi-stage Sim-to-Real transfer learning, and physics-informed regularization to enhance the predictive accuracy and physical consistency. A variety of spatiotemporal architectures were assessed, such as transformer-based and recurrent-convolutional ones, alongside synthetic pretraining,silver-label adaptation, and expert fine-tuning. The results show that transformer-based architectures outperformed in terms of the accuracy of the instantaneous prediction, while lightweight recurrent-convolutional architectures achieved higher temporal stability and operational oceanographic skill. Ablation studies also demonstrated the benefits of physics-guided regularization in terms of trend-following consistency, and physically implausible predictions. Explainability auditing also helped to focus attention in hydrodynamically active surf-zone regions and showed good agreement with the physically derived wave propagation behavior. In general, the proposed framework shows the promise of physics-guided video-based deep learning systems for long-term coastal wave monitoring that are cost-efficient and operationally feasible.

Abubakar Hamisu Kamagata, Dharm Singh Jat, Attlee Munyaradzi Gamundani +2

Computer Science, Namibia University of Science and Technology, 13 Jackson Kaujeua Street, Windhoek, 13388, Windhoek, Namibia. · Computer Science Engineering, Indian Institute of Technology Indore,2026 Khandwa Road, Simrol, Indore, 453552, Madhya Pradesh, India. · Namdeb 1906, Windhoek, Namibia.

Physics-Informed ML

Jun 11, 2026math.NA

Neural Architectures as Functional Priors in Physics-Informed Control Problems

In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations. Rather than focusing on highly complex problems, our objective is to investigate architecture-dependent effects in controlled dynamical systems within the simplest physically interpretable settings possible. In particular, we study a controlled linear RLC electrical circuit and a nonlinear Duffing-type dynamical system. Both systems are analyzed first through classical optimal-control formulations and later through PINN-based approaches. We compare different combinations of multilayer perceptrons (MLPs) and Fourier-based KAN-like architectures, and analyze their influence on the resulting controls. The numerical experiments suggest that different architectural choices systematically generate qualitatively distinct controls, even under identical governing equations, loss functionals, initial and target states, training parameters and physical constraints. Significant differences appear in the spectral structure, smoothness, energy distribution, and phase-space behavior of the learned solutions. A central observation of this work is the emergence of a functional specialization phenomenon when the neural architectures are allowed sufficient freedom to shape the structure of the learned controls. More specifically, in the systems considered here, Fourier-based architectures tend to produce trajectories with richer oscillatory content, whereas smoother low-frequency-biased architectures tend to generate more regular and energetically efficient controls. This suggests that different functional components of the control problem may be handled more efficiently by different neural architectures, leading to an implicit specialization between state representation and control generation.

Sonia Rubio Herranz, Fernando Carlos López Hernández, Antonio López Montes

Department of Statistics and Operations Research (EIO), Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Software Engineering and Artificial Intelligence, Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Analysis and Applied Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain

Dynamical Systems Physics-Informed ML Optimal Control

Jun 11, 2026eess.SY

MPC for underactuated spacecraft control with a Lyapunov supervised physics-informed neural network correction layer

Underactuated spacecraft faces controllability limitations and heightened sensitivity to environmental disturbances, complicating attitude maneuvering and stabilization. Due to the lack of control authority along the underactuated axis, conventional controllers cannot directly stabilize all attitude components and therefore require reference planning strategies. Furthermore, MPC approaches remain sensitive to inertia uncertainty and unmodeled dynamic couplings, resulting in degraded tracking performance under mismatch. To address these issues, we consider a hierarchical architecture integrating three layers: (i) a nonlinear model predictive controller (NMPC) for constraint and underactuation-aware maneuver planning and nominal closed-loop stability under actuator limits; (ii) a physics-informed neural network (PINN) trained offline on simulation data to estimate residual disturbance torques, with loss terms that enforce consistency with rigid-body rotational dynamics; (iii) a Lyapunov-based supervisory safety mechanism that evaluates the learned correction online and bounds or suppresses its influence to preserve the stability properties of the baseline controller. The architecture is evaluated in a high-fidelity simulation environment modelling reaction wheel dynamics, actuator saturation, and environmental disturbances. Monte Carlo studies show statistically significant reductions in steady-state attitude error relative to standalone NMPC while maintaining robust behavior under uncertainty. The supervisory layer ensures graceful degradation to purely model-based control when the learning-based augmentation is unreliable.

Amirhossein Ayanmanesh Motlaghmofrad, Carlo Cena, Mauro Martini +1

Politecnico di Torino, Torino (TO), ITA · Argotec S.R.L., San Mauro (TO), ITA

Nonlinear MPC Feedback Control Physics-Informed ML

Jun 10, 2026cs.LG

Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources

Physics-Informed Neural Networks (PINNs) are a machine learning method for solving forward and inverse Partial Differential Equations (PDEs). When applied to PDEs with Dirac delta functions in the forcing terms, boundary conditions, or initial conditions, PINNs require approximating them with smooth surrogate functions, a practice that can introduce significant modeling errors. In this work, we exploit the interpretation of PINNs as Residual Least Squares (RLS) methods and show that this perspective enables direct treatment of Dirac delta terms by integrating the weak-form equation. Among RLS formulations other than PINN, we focus on the Radial Basis Function (RBF) expansion (also known as a single-layer RBF Network). We show that while integrating out the Dirac delta in PINNs causes residuals to fail to converge to zero, RBF-RLS consistently provides good forward and inverse solutions to transport problems. We explain this finding using the Neural Tangent Kernel (NTK) theory. We test both approaches on linear PDEs that represent groundwater flow and transport in porous media and rivers. We solve inverse problems to fit synthetic data, noisy synthetic data, and real-world measurements.

Manuel Reyna, Alexandre Tartakovsky

Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, 205 North Mathews Avenue, Urbana, 61801, IL, USA

PDE Solving Physics-Informed ML PDE Inverse Problems Radial Basis Function Networks

Jun 10, 2026cs.LG

Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability

Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

Riya Bisht, Dhruv Agarwal

Dynamical Systems Parameter Estimation Parameter Identifiability Physics-Informed ML

Jun 10, 2026cs.LG

Physics-Aware Auxiliary Losses Improve Out-of-Distribution Generalization of a GNN Synthesizability Filter

Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.

Riya Bisht, Dhruv Agarwal

Graph Neural Networks OOD Generalization Physics-Informed ML Molecular Property Prediction Physics-Informed GNNs

Jun 10, 2026math.NA

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative. Their relative performance remains difficult to assess because the two approaches are often compared under different formulations, parameterizations, optimizers, and regularization choices. We present a fair comparison of adjoint optimization and PINNs for PDE-constrained inverse problems. From a common abstract formulation, we instantiate both methods on identical domains, governing equations, observation models, and regularization terms, while matching the optimizer, unknown parameterization, and arithmetic precision wherever applicable. The benchmarks include unsteady Burgers, noisy Darcy permeability inversion, three-dimensional Allen--Cahn reaction identification, and unsteady Navier--Stokes viscosity identification. The results show that the representation of the unknown largely determines the preferred method: grid-based fields favor the discrete adjoint, whereas neural representations are native to PINNs and relevant for closure and constitutive modeling. For time-dependent problems, adjoint inversion can be dominated by trajectory storage and differentiation, while PINNs provide satisfactory reconstructions at lower cost. A PINN-warm-started adjoint strategy then recovers adjoint-level accuracy at substantially reduced cost.

Zhen Zhang, Alessandro Alla, George Em Karniadakis

Division of Applied Mathematic, Brown University, Providence, RI, USA · Department of Mathematics, Sapienza Università di Roma, Rome, Italy

Constrained Optimization Physics-Informed ML PDE Inverse Problems

Jun 10, 2026cs.CV

An Electric Potential-Augmented Benchmark Dataset for Physics-Guided Image Reconstruction of Electrical Capacitance Tomography

While deep learning has significantly advanced image reconstruction of Electrical Capacitance Tomography (ECT), most data-driven methods map directly between capacitance and permittivity distribution, treating the sensor as a black box. This overlooks the electric potential field -- the fundamental physical link governing the nonlinear and ill-posed ``soft-field'' effect. To address this, we propose an electric potential-augmented ECT benchmark dataset designed to explicitly integrate latent physics behind ECT into the learning process. Generated via a COMSOL-MATLAB pipeline for an eight-electrode sensor as an example, the dataset comprises 20,000 randomized samples across four typical flow patterns. Crucially, alongside the conventional capacitance vectors and permittivity distributions depicted as images, each sample preserves eight excitation-wise full-field potential maps. Beyond data release, we provide illustrative evaluation protocols for both forward and inverse problems of ECT. Through comprehensive testing on both in-distribution (IID) and out-of-distribution (OOD) scenarios, we systematically demonstrate how the inclusion of electric potential maps enhances modeling accuracy and robustness. Fundamentally, the explicit inclusion of latent field information significantly lowers the barrier to integrating physical laws into ECT modeling, thereby establishing a standardized foundation for future physics-guided machine learning of ECT image reconstruction.

Xinqi Zhang, Qiming Ma, Lihui Peng

Department of Automation, Tsinghua University, Beijing 100084, China

Image Reconstruction Physics-Informed ML Computed Tomography

Jun 10, 2026cs.LG

Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} upper bounds for PINN prediction errors, complete certification also requires complementary lower information in order to obtain computable two-sided error enclosures. In this paper, we derive computable \emph{a posteriori} lower bounds for PINN errors in ordinary differential equations on suitable certified state-space domains under a localized strong monotonicity condition. We combine these estimates with complementary localized upper bounds under a one-sided Lipschitz condition, which is weaker than the global Lipschitz assumption used in previous work and can yield sharper upper error bands. The resulting bounds depend only on the neural-network approximation, the ODE residual, and local monotonicity and growth constants, and therefore do not require access to the exact solution. For linear time-invariant and time-varying systems, we further derive explicit formulas in terms of the minimal and maximal eigenvalues of the symmetric part of the system matrix. We also discuss the distinction between soft and hard enforcement of initial conditions in PINNs and explain why exact enforcement can make the scalar lower certificate uninformative. To recover nontrivial lower information in the linear setting, we use a signed-residual finite-probe certificate based on coordinate unit vectors. We also formulate a certificate-informed training strategy in which the propagated upper certificate is used as an auxiliary regularizer, while lower certificates remain post-training diagnostics. Altogether, the proposed framework provides rigorous and practically computable error certificates for PINN approximations of ODEs, while making explicit the domains and model classes for which the assumptions can be verified.

Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov

Physikalisch-Technische Bundesanstalt (PTB), Germany · Technical University of Berlin, Germany · Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany +1

Dynamical Systems Neural Network Verification Physics-Informed ML

Jun 10, 2026cs.LG

Physics-Distilled Neural Network enabled by Large Language Models for Manufacturing Process-Property Predictive Modeling

Predicting process-property relationships in manufacturing is often challenged by high experimental costs and the limited interpretability of complex 'black-box' models. This paper proposes a novel knowledge distillation framework designed to achieve high-accuracy predictions in data-scarce scenarios. The framework integrates analytical physics priors, which are systematically extracted from scientific literature via Large Language Models, into a privileged teacher model. We employ a Graph-Masked Attention layer to capture the complex physical dependencies among input variables showing strict setpoints or a combination of static and high-frequency temporal signatures. This privileged knowledge is distilled into a lightweight student predictor for inference. The feasibility and robustness of the framework are evaluated through a comprehensive experiment across five diverse manufacturing processes. To ensure statistical reliability, given the small dataset sizes, a repeated K-fold cross-validation technique is employed to quantify model stability and generalization. Results indicate that the proposed framework consistently achieves high predictive accuracy across all evaluated domains. Most importantly, the architecture demonstrates significant fault tolerance by maintaining robust predictive performance even in scenarios where LLM-derived analytical priors are suboptimal or incomplete. Furthermore, the student predictor achieves an inference frequency exceeding 6000 Hz, which facilitates real-time edge deployment on standard industrial hardware. This work provides a scalable solution for bridging the gap between theoretical physics and real-time industrial monitoring in data-limited environments.

Ge Song, Kiarash Naghavi Khanghah, Anandkumar Patel +2

School of Mechanical, Aerospace and Manufacturing Engineering, University of Connecticut, Storrs, CT 06269 · Department of Mechanical & Aerospace Engineering, Rutgers, the State University of New Jersey, Piscataway, NJ 08854

Neural Surrogate Modeling Materials Property Prediction Physics-Informed ML Knowledge Distillation

Jun 9, 2026cs.LG

SwiftCTS: Fast Cross-Design Prediction and Pareto Optimization of Clock Tree Metrics via Few-Shot Calibration

Clock Tree Synthesis (CTS) is a computationally expensive stage in the physical design flow, requiring iterative EDA tool invocations to navigate a vast configuration space for optimal power, wirelength, and timing skew. Existing machine learning approaches require computationally expensive retraining or fine-tuning cycles to adapt to unseen macro architectures and are architecturally mismatched to the millions of evaluations demanded by exhaustive combinatorial search. We present SwiftCTS, a physics-informed surrogate framework that addresses both limitations simultaneously. By coupling lightweight, physics-grounded statistical features with gradient-boosted ensembles, SwiftCTS trains in under five seconds on a CPU and delivers sub-millisecond inference without GPU support. To handle out-of-distribution (OOD) designs without retraining or fine-tuning, we introduce a K-shot multiplicative calibration mechanism that anchors predictions to just one or two physical reference runs, reducing power prediction error from 24.5% to 3.3% and wirelength error from 56.6% to under 1% on unseen macros. Integrating this engine with an evolutionary optimizer, SwiftCTS evaluates 100,000 CTS configurations in under ten seconds, yielding Pareto-optimal frontiers that are physically validated within the OpenROAD flow. Closed-loop validation confirms prediction errors below 0.5% for power and wirelength, and timing skew predictions within five picoseconds on an OOD benchmark, consistently outperforming default tool heuristics across all target metrics. Code publicly available at: https://github.com/BarsatKhadka/SwiftCTS

Barsat Khadka, Kawsher Roxy, Md Rubel Ahmed

The University of Southern Mississippi Hattiesburg, MS, USA · Intel Corporation Hillsboro, OR, USA · Louisiana Tech University Ruston, LA, USA

Surrogate Modeling Surrogate-Assisted Optimization Model Calibration Physics-Informed ML

Jun 9, 2026cs.LG

Population-Aware Physics-Informed Neural Particle Flow for Bayesian Update

Physics-informed neural particle flow (PINPF) learns a deterministic transport field that moves particles from a prior distribution toward a Bayesian posterior while enforcing the governing probability-evolution equation. However, the standard PINPF velocity model processes particles independently and therefore does not explicitly condition its transport decisions on the empirical particle population. This paper introduces population-aware PINPF (PA-PINPF), which augments each particle update with a permutation-invariant Deep Sets representation of the full particle set. We investigate two population encoders. PA-PINPF-State summarizes the particle states, whereas PA-PINPF-Feature summarizes the complete local physics-informed feature vectors, including particle position, pseudo-time, measurement information, likelihood values, and score information. The latter allows the population context to represent not only particle-cloud geometry, but also the population-level Bayesian transport geometry. The methods retain the original unsupervised physics-informed residual objective and require no ground-truth posterior samples during training. Experiments on range-measurement tasks and nonlinear time-difference-of-arrival posterior transport demonstrate that both population-aware variants improve over particle-wise PINPF, while feature-population encoding provides the strongest performance. These results show that population-level physics features provide useful global information for learned Bayesian particle transport.

Batu Candan, Simone Servadio

Iowa State University, Ames, IA 50011, USA

Bayesian Inference Deep Sets Physics-Informed ML

Jun 9, 2026cs.CE

Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.

Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière +3

Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, Talence, France · Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence, France · Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, 09599, Germany +2

Neural Surrogate Modeling Structural Mechanics Physics-Informed ML Physics-Informed GNNs Spatiotemporal GNNs

Jun 9, 2026cs.LG

Least-Action-Guided Diffusion for Physical Extrapolation

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

Zhongxin Yang, Yuanwei Bin, Xiang I. A. Yang +1

College of Engineering, Peking University, Beijing 100871, China · Ningbo Institute for Digital Twin, Eastern Institute of Technology, Ningbo 315200, Zhejiang, China · Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo 315200, Zhejiang, China +2

Physics-Informed Diffusion Models Physics-Informed Generative Modeling Diffusion Guidance PDE Surrogate Modeling OOD Generalization Physics-Informed ML

Jun 9, 2026physics.comp-ph

An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks

The pulsar magnetosphere has only recently been addressed using Physics-Informed Neural Networks (PINNs), by deploying a domain-decomposition approach and treating the separatrix and equatorial current sheet as infinitesimally thin discontinuities. However, this baseline requires extensive manual hyperparameter tuning, achieves limited final accuracy and demands several hours of training. We refine this framework by introducing domain-specific neural architectures based on Kolmogorov-Arnold networks, an automated adaptive training pipeline and a physics-based convergence criterion that eliminate the need for manual calibration. The proposed methodology delivers self-consistent axisymmetric magnetosphere solutions with mean squared errors of the PDE residuals at O(1e-6) in double precision - an improvement of two orders of magnitude over the baseline - while achieving convergence in under 20 minutes in single precision. Importantly, the method reliably resolves stellar radii reduced by up to 80% compared to the baseline, overcoming the severe spatial scale disparities that also challenge traditional solvers. Furthermore, by varying the flux that opens to infinity, we provide a correction to the equation that connects it to the equatorial T-point's position. The complete framework is released as the open-source library PulsarX.

Spyros Rigas, Ioannis Contopoulos, Georgios Alexandridis +1

Department of Digital Industry Technologies, School of Science, National and Kapodistrian University of Athens, 34400 Psachna, Greece · Research Center for Astronomy and Applied Mathematics, Academy of Athens, 11527 Athens, Greece

Neural PDE Solvers Physics-Informed ML

Jun 9, 2026cs.LG

PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection

While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.

Fateme Mohammad Mohammadi, Hector Budman, Joshua L. Pulsipher

Department of Chemical Engineering University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada

Neural Surrogate Modeling Constrained Optimization Physics-Informed ML