Scientific ML

ML: Machine Learning

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9 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 84

Oct 8, 2026hep-ph

Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery

Machine learning (ML) in high-energy nuclear physics (HENP) is entering a new stage in which physical knowledge is incorporated more directly into data analysis, simulation, and physics inference. This mini-review focuses on developments that have matured in the past several years. Whereas earlier applications emphasized event classification, pattern recognition, and surrogate models for selected observables, recent work has moved toward physics-integrated workflows: calibrated Bayesian extraction of QCD matter properties, dense-matter equation-of-state inference from heavy-ion and neutron-star data, generative event modeling, neural unfolding of weak physical signals, differentiable inverse solvers, gauge-equivariant and diffusion-based lattice-field samplers, and neural reconstruction of model functions in holographic QCD. We survey recent applications of ML in heavy-ion collisions, neutron-star physics, lattice QFT, and holographic or continuum QCD. The emphasis is not on ML architectures alone, but on how they enter concrete physics workflows, how physical constraints such as symmetries, conservation laws, causality, thermodynamic stability, and topology are imposed, and how uncertainty quantification and validation determine whether an AI-assisted result can support a reliable physics conclusion.

Xun Chen, Weiyao Ke, Yu-Gang Ma +2

School of Nuclear Science and Technology, University of South China, Hengyang 421001, China · INFN — Istituto Nazionale di Fisica Nucleare — Sezione di Bari, Via Orabona 4, 70125 Bari, Italy · Key Laboratory of Quark and Lepton Physics (MOE) & Institute of Particle Physics, Central China Normal University, Wuhan, Hubei 430079, China +6

High-Energy Physics Physics-Informed ML Scientific ML Physics-Informed Generative Modeling

Oct 8, 2026cond-mat.soft

A structure-preserving neural density functional for the ions of a polymer electrolyte

Predicting the structure and response of inhomogeneous polymer electrolytes requires a description of ion correlations that retains molecular-scale accuracy while remaining transferable across spatial scales and geometries. We develop a neural density functional for electrolytes that preserves spatial symmetries, thermodynamic integrability and the Noether identities, with perfect screening recovered in stable, noncritical bulk states. Its nonlinear density dependence captures the concentration-dependent correlations missed by a pair closure, including a crossover from enhanced to suppressed long-wavelength number fluctuations at strong coupling. The functional describes density profiles at an untrained salt concentration and predicts bulk structure factors and the long-wavelength number response. Trained solely on planar density and internal-force profiles from molecular dynamics, the functional predicts ionic structure in larger domains and in two-dimensional external fields. On the same ion data, it is more accurate than three other neural density-functional architectures and keeps its accuracy with a quarter of the training runs, where the errors of the best alternative grow by about two thirds. The spatial transferability provides a necessary foundation for connecting molecular correlations to continuum predictions at larger scales.

Liyao Lyu

School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei, Anhui, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou, Jiangsu, China · Suzhou Big Data & AI Research and Engineering Center, Suzhou, Jiangsu, China

Materials Science Scientific ML

Oct 5, 2026cs.LG

Data, Numbers, and Geometry: Three Tutorials on Numerical Methods, Machine Learning, and Evaluation

We present three practical tutorials on numerical computation and machine learning for mathematical research, developed for the DANGER: Data, Numbers, and Geometry workshop held at the Banff International Research Station in April 2026. The first develops a numerical approach to exterior calculus from pointwise evaluations of differential forms, using a flux formulation of the exterior derivative. Examples in Euclidean space and on the sphere illustrate geometric identities, topological features, and the effects of approximation and finite precision. The second examines how mathematical structure guides neural network design through examples involving elliptic curves, quivers, and a boundary value problem. It explores how architectural choices affect learning and uses interval arithmetic to bound the residual of a trained network over the full interval of the boundary value problem. The third addresses the evaluation and presentation of machine learning results, covering performance metrics, statistical uncertainty, classification thresholds, receiver operating characteristic curves, and accessible figure design. Throughout, the tutorials distinguish numerical agreement, predictive accuracy, structural guarantees, and rigorous bounds as different forms of evidence. Each contribution can be read independently, with accompanying notebooks and exercises that allow readers to reproduce the examples and adapt the methods to other problems.

Jessica N. Howard, Yidi Qi, Tomás S. R. Silva

Instituto de Matemática, Estatística e Computação Científica (IMECC), Universidade Estadual de Campinas (UNICAMP), Rua Sérgio Buarque de Holanda, 651, 13083-859 Campinas, São Paulo, Brazil

Oct 5, 2026math.NA

An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations

Systems of equations arise in a wide range of scientific and engineering applications. The present work focuses on solvers for general systems of equations, including but not limited to those arising from partial differential equations. These systems can be broadly categorized into linear and nonlinear problems. For large linear systems, iterative solvers are generally preferred over direct methods due to the latter's superlinear growth of computational costs. Although convergence theory is well-developed under certain assumptions on the coefficient matrix, many classes of systems still pose open challenges. These difficulties become even more severe for systems of nonlinear equations, where nonlinear solvers typically rely on repeated linearization. For example, Newton's method may even converge quadratically near the solution; it can also converge slowly or diverge when the initial guess is not chosen appropriately. A wide range of solvers with diverse variants and hyperparameter settings exists, and the development of efficient and robust iterative methods remains an active area of research. Recently, machine learning (ML) techniques have been applied to enhance the efficiency of classical iterative methods while preserving their interpretability and reliability. We refer to these ML-enhanced iterative methods as hybrid iterative methods, in the sense that they combine classical iterative methods with ML. This paper provides a comprehensive overview of state-of-the-art approaches to constructing hybrid iterative methods for systems of both linear and nonlinear equations, while also discussing open challenges and outlining potential directions for future research.

Yuhuang Meng, Jing Zhao, Alexander Heinlein

Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, the Netherlands · Department of Hydrodynamics and Forecasting, Deltares, Boussinesqweg 1, Delft, 2629 HV, the Netherlands

Learning to Optimize Scientific ML

Oct 1, 2026cs.AI

Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering

The rapid maturation of artificial intelligence (AI) and machine learning (ML) has catalyzed a profound shift in how chemical engineering problems are formulated, analyzed, and solved. Advances in computing, data availability, and learning algorithms have enabled AI/ML methods to impact applications spanning atomic-scale simulations, materials and catalyst discovery, transport and thermodynamics, separations, process systems engineering, and industrial operations. This article provides a perspective on recent methodological developments and representative applications, emphasizing how AI/ML tools are being integrated with first-principles models to address challenges of predictive accuracy, data scarcity, extrapolation, interpretability, and model lifecycle management. Across domains, a unifying trend is the move away from purely black-box approaches toward hybrid and physics-informed frameworks that explicitly respect conservation laws, thermodynamic consistency, and known structural constraints. These approaches not only improve robustness and reliability, but also enable meaningful human-AI collaboration by providing information at an appropriate level of abstraction for the task and decision context. We conclude that AI and ML are not replacing the core principles of chemical engineering; rather, they are amplifying them. As the field advances toward increasingly autonomous, adaptive, and sustainable systems, the thoughtful integration of AI/ML with first-principles understanding and domain expertise will be essential to realizing their full potential across both research and industrial practice.

Michael Baldea, Linda J. Broadbelt, Marianthi G. Ierapetritou +17

McKetta Department of Chemical Engineering and Oden Institute for Chemical Engineering and Sciences, The University of Texas at Austin, Austin, TX 78731, USA · Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA · Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE 19716, USA +13

Scientific ML Physics-Informed ML

Sep 30, 2026cs.LG

A library for differentiable signal processing and machine learning on the sphere

The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, including geophysics, planetary science, geodesy, atmospheric physics, quantum chemistry, cosmology, and virtual reality, among many others. As machine learning increasingly permeates these fields, the demand grows for robust tools that process and model functions on the sphere, while respecting the inherent topological and symmetry properties of the domain. We present torch-harmonics, a comprehensive library that offers efficient, differentiable implementations of advanced signal processing and machine learning (ML) methods for spherical data. These include the spherical harmonic transform (SHT), the spherical analogue of the Fourier transform, vector spherical harmonics, discrete-continuous and spectral convolutions, as well as both global and neighborhood spherical attention mechanisms. Beyond traditional representations, torch-harmonics provides the building blocks for state-of-the-art spherical ML architectures such as spherical transformers in order to enable scalable, rotationally-aware learning and inference in modern scientific and engineering applications.

Thorsten Kurth, Max Rietmann, Mauro Bisson +6

NVIDIA Corporation · California Institute of Technology

Geometric Representation Learning Spherical Harmonics Scientific ML

Sep 30, 2026physics.chem-ph

A strategic roadmap for an atomistic machine-learning ecosystem

Data-driven machine learning (ML) techniques have become an essential tool in many domains of science. Their application to atomistic simulations of matter is particularly widespread and impactful. This success is due largely to the existence of a well-developed and established physics-based modeling framework, ranging from first-principles electronic-structure calculations to molecular dynamics and statistical sampling, into which ML was integrated naturally to reshape long-standing trade-offs between accuracy, efficiency, and scale. Nevertheless, this integration raises both conceptual and practical challenges, from choosing between data-centric and physics-based modeling approaches to adapting established software stacks to modern hardware accelerators and ML libraries. As the field evolves rapidly, fueled in part by widespread enthusiasm but also by tangible impact, it seems appropriate to take a moment to consider the current state of the art and open challenges, and reflect on what can be done to better coordinate efforts across the community. With this goal in mind, several members of this community met in Lausanne in January 2026 at CECAM to discuss algorithms, models, software and hardware infrastructure, and the most promising scientific applications that have become possible thanks to the use of artificial intelligence in atomic-scale simulations. This strategic roadmap paper summarizes the outcomes of these discussions, suggesting some long-term goals, and some concrete actions, to establish a healthy, sustainable and impactful atomistic ML ecosystem.

Jörg Behler, Michele Ceriotti, Cecilia Clementi +46

Machine Learning Interatomic Potentials Scientific ML Computational Materials Science

Sep 28, 2026cs.LG

ALICE: In-context, Zero-shot, Mutual Information Estimation

Estimating mutual information (MI) from samples is a central objective in a variety of scientific fields. Modern neural estimators are accurate in the large-data regime, but they fall short when data is scarce, and each must be fit anew for every distribution under study. Current estimators are moreover tied to specific data types. These constraints limit their adoption in many applications where per-distribution training is impractical and sample sizes are small. We present ALICE, a foundation model that removes per-distribution training, while achieving competitive estimation accuracy. Trained exclusively on a broad family of synthetic distributions, ALICE acts as an in-context estimator of rectified-flow velocity fields: conditioned on samples of an unseen distribution, it estimates that distribution's velocity field without any explicit training. MI is then obtained through a fixed identity that integrates the squared difference between the joint and conditional fields. We validate ALICE on a standard, challenging benchmark and apply it in three domains, biology, genetics, and neuroscience, whose data the model has never seen. For the first time, we show that a single model closes the gap with neural estimators trained separately for each distribution, while natively supporting different data dimensionality and sample cardinality, enabling zero-shot MI analysis across scientific domains.

Giulio Franzese, Simone Rossi, Pietro Michiardi

EURECOM, Sophia Antipolis, France

Zero-Shot Learning In-Context Learning Scientific ML Mutual Information Estimation

Sep 27, 2026cs.LG

The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning

Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness in the mathematical sense is not the same as fidelity to the physics. Here I argue that a derivative can be numerically perfect and still be the wrong derivative for the problem at hand, because AD, by construction, has no notion of the physical structure a solution must obey. Convection and its associated directionality, diffusion, and dispersion are only the most visible instances of a much longer list that spans all branches of computational science and engineering, including conservation, thermodynamic consistency, symmetry, symplectic structure, positivity, monotonicity, and boundedness. Recognizing this broader gap reframes how the field should build the next generation of PDE-driven neural surrogates.

Ameya D. Jagtap

Aerospace Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA

Automatic Differentiation PDE Surrogate Modeling Scientific ML Physics-Informed ML

Sep 23, 2026cs.LG

The Mechanics of Delta Learning: Target Design for Generalizable Scientific Machine Learning

In scientific machine learning,

Δ

-learning trains models on residual errors relative to physical baselines, assuming that more accurate baselines with smaller residual scales inherently improve downstream performance. Here, we demonstrate that residual scale alone is an insufficient heuristic for learnability. Evaluating molecular graph neural networks on total energy targets, we show that complex local descriptor baselines can yield small residual targets that are disproportionately rough within architecture-informed proxy spaces and harder to learn relative to their scale. Conversely, semi-empirical baseline reduces both scale and normalized roughness, improving in-domain and out-of-domain prediction. We introduce scale-normalized graph Dirichlet roughness (

D_{\text{IQR}}

) as a pre-training diagnostic for residual learnability and establish baseline complementarity as a core target-design principle, elevating target space formulation alongside model architecture as a key axis for scientific machine learning.

Kareem M. Gameel, Ihor Neporozhnii, Sjoerd Hoogland +1

Department of Physical and Environmental Sciences, University of Toronto Scarborough Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada · Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada · Department of Chemistry, University of Toronto Department of Physical and Environmental Sciences, University of Toronto Scarborough Alliance for AI-Accelerated Materials Discovery (A3MD) Toronto, Ontario, Canada

Residual Learning Scientific ML Molecular Property Prediction

Sep 22, 2026cs.LG

Targeted Review for AI-Assisted Biodiversity Surveys: Active Continuous-Score Occupancy Modeling

We increasingly use machine learning to label scientific datasets. The models we develop and deploy are improving all the time, but they are not and will likely never be perfect. Mistakes matter, as errors can propagate into our scientific understanding, particularly when systematically biased. Very reasonably, scientists thus review substantial proportions of ML-generated labels to verify or correct mistakes in pursuit of ensuring their scientific findings are not biased by ML. In this work, we focus on helping scientists optimally allocate this reviewing effort relative to their scientific goals. We focus on a specific class of scientists (ecologists) and a specific, widespread, and impactful modeling target (occupancy modeling, which estimates where species are likely to occur, conditioned on environmental factors). We introduce Active Continuous-Score Occupancy Modeling (ACORN), a method that incorporates ML predictions into occupancy models and strategically selects samples for expert review that are maximally informative for downstream ecological analysis. Across camera-trap and bioacoustic datasets, our method recovers ecological conclusions close to those obtained from fully human-labeled data, while requiring substantially fewer expert reviews than non-targeted review policies. Our results suggest that ML-assisted scientific workflows should optimize expert effort for downstream inference, rather than for classifier accuracy alone, especially when human review budget is limited. Our code is available at https://github.com/timmh/acorn

Timm Haucke, Lauren Harrell, Justin Kay +2

MIT · Google Research · The Institute for Bird Populations

Active Learning Human-in-the-Loop AI Scientific ML Wildlife Monitoring

Sep 14, 2026cs.AI

Hybrid Physics-AI Framework of Body Center of Mass Dynamics from Wrist-Worn Sensors

Wrist-worn IMU has been widely used for daily-life health monitoring. Yet, it does not fully represent whole-body dynamics, for which the body center of mass (COM) is considered the physiological reference standard. Therefore, this work proposes a simplified kinematic model (KM), which is designed to map the wrist IMU to the COM acceleration. It is built upon several reductive assumptions that enable the solvability of the dynamic equations based on wrist IMU measurements alone. This work further proposes three types of hybrid AI modeling methods, namely human kinematic model-based neural network (HKM-NN) models, to leverage the power of both grey-box and black-box modeling. The HKM-NN methods include serial learning (ser-) and two approaches of simultaneous learning (sim1- and sim2-). The proposed models are trained and tested using our dataset, which includes wrist IMU measurements and ground-truth COM measurements from 10 healthy volunteers during six gait activities and sit-to-stand (SS) transitional movement. The results demonstrate the feasibility of estimating COM acceleration from wrist IMU measurements. Our KM model yields satisfactory results, with an error ranging from 6.7% to 12.5% for gait activities and 5.6% for the SS. In comparison with the KM model, our HKM-NN models significantly enhance the performance, achieving 5.3% to 9.3% errors for gait activities, and the best error of 3.9% for the SS. In addition, the HKM-NN models demonstrate distinct robustness characteristics under noisy test conditions, with sim1-/sim2- generally maintaining greater robustness under Gaussian perturbations, while the KM model exhibits comparatively strong robustness under salt-and-pepper noise. These findings highlight the importance of combining biomechanical structure with data-driven learning for wearable sensing applications operating under imperfect and noisy measurement conditions.

Shuhao Que, Valentina Breschi, Ying Wang

Electrical Engineering, University of Twente, Drienerlolaan 5, Enschede, 7522 NB, Netherlands. · Electrical Engineering, Eindhoven University of Technology, Groene Loper 19, Eindhoven, 5612 AP, Netherlands.

Gait Analysis Wearable Sensing Scientific ML

Sep 7, 2026physics.geo-ph

SeisBench DAS: A machine learning framework for Distributed Acoustic Sensing

Fibre optic sensing, such as distributed acoustic sensing (DAS), has become a widespread technology for geophysical studies. To process the large-scale datasets produced by DAS, several machine learning methods have been proposed. However, without standardization of data and models, these methods lack comparability and interoperability. This introduces a gap between model developers and practitioners analyzing DAS data and inhibits adoption of deep learning for DAS. To address these limitations, here we present SeisBench DAS, an extension to the SeisBench library for machine learning in seismology. SeisBench DAS defines standard formats for DAS benchmark datasets, including standardised metadata and labels, and DAS models. It builds on the xdas framework for data ingestion and virtual array handling, and on PyTorch for reading and applying the machine learning models. Importantly, SeisBench provides an engine to efficiently apply deep learning models to diverse formats of DAS data, bridging the gap between model developers and practitioners. SeisBench DAS is designed as an open and extensible framework, allowing to easily incorporate future developments in deep learning for DAS.

Jannes Münchmeyer, Han Xiao, Frederik Tilmann

GFZ Helmholtz Centre for Geosciences · Institute for Geological Sciences, Freie Universität Berlin, Berlin, Germany

Distributed Acoustic Sensing Scientific ML Seismology

Sep 1, 2026cs.LG

Neural Symbollic Regression Using Deep Learning and Sparse Modelling

Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.

Ravi Kumar U, Sumitra S

Department of Mathematics Indian Institute of Space Science and Technology Thiruvananthapuram, India

Scientific ML Neurosymbolic Learning Symbolic Regression

Aug 13, 2026cs.LG

Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations

In order to understand complex systems such as the human metabolome or human brain, different sensing technologies are used, generating complex data. These datasets are often multiway, i.e., with more than two axes of variation such as a subjects by metabolites by time array. While tensor factorizations have successfully revealed interpretable patterns from such complex data, they have so far been mainly data-driven. On the other hand, there is more to data -- there are computational models (of these systems), which are rich sources of prior information. In this paper, we introduce a knowledge-guided approach that brings together data and computational models by jointly analyzing real data and simulated data (generated using a computational model) using coupled tensor factorizations with linear coupling. Our experiments on real metabolomics measurements demonstrate that guiding the analysis of such noisy data with simulated data improves the pattern discovery performance while also revealing potential discrepancies between data and computational models.

Gaute Johannessen, Geert Roelof van der Ploeg, Evrim Acar

Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo · Department of Data Science and Knowledge Discovery, Simula Metropolitan Center for Digital Engineering, Oslo

Tensor Decomposition Scientific ML

Aug 6, 2026cs.LG

SEAM: Global consistency beyond local accuracy in scientific machine learning

Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction. Yet such local checks cannot establish whether the resulting explanations can be assembled into one globally admissible explanation. We introduce Scientific Explanation-Admissibility Machines (SEAM), a generator-agnostic framework that makes this local-to-global consistency question computable across regions, sensors, regimes, and model components. The finite explanation-sheaf instantiation SEAM-

Ω

represents each region by a structured explanation with state, closure, and observation channels together with optional contract metadata; compares neighboring explanations on their overlaps; and converts disagreement into a channel-resolved obstruction. This obstruction locates inconsistency and tests competing declared accounts by restricting each repair to the revisions that one account permits. Exact feasibility refutes or retains an account; when exact repair is unavailable, residual-aware regularized records provide a separately labeled empirical attribution. The framework also separates inconsistency from non-identifiability and monitors learned generators under distribution shift. We establish theorems for minimum-cost intervention and conservation-contract detectability, together with companion results for identifiability and closure recoverability. Across nineteen experiments involving synthetic partial differential equation systems and out-of-distribution Fourier neural operator (FNO) monitoring, SEAM detects incompatible explanations even when local predictions are accurate, and attributes failures to specific channels and overlaps. SEAM adds a global explanation-consistency audit to existing solvers and learning models, testing whether their local explanations form a coherent scientific account.

Gnankan Landry Regis N'guessan, Bum Jun Kim

Axiom Research Group · Department of Applied Mathematics and Computational Science, The Nelson Mandela African Institution of Science and Technology, 404 Nganana, Kikwe, Arumeru, P.O. Box 447, Arusha, 23311, Tanzania · African Institute for Mathematical Sciences, Research and Innovation Centre, KN 3 Road, Gasharu Cell, Kicukiro Sector, Kicukiro District, Kigali, Rwanda +1

Multi-View Consistency Explainable Artificial Intelligence Scientific ML

Aug 5, 2026cs.LG

When Proxy Prediction Becomes Equation Reconstruction: Diagnostics and Residual Learning for Factor-Derived Proxy Supervision

Scientific machine learning often relies on proxy targets computed from known domain factors when direct observations are limited. When those same factors are used as model inputs, however, high predictive accuracy may reflect reconstruction of the proxy-generating equation rather than robustness to degraded factor information. We study this problem in RUSLE-derived soil-loss proxy prediction under controlled degradation of the soil-erodibility factor

K

. We introduce a diagnostic framework that combines degraded-formula references, classical tree-based baselines, matched direct and formula-feature predictors, contextual ablations, tail-error analysis, and degradation robustness scoring. We then propose RASPL, a formula-preserving residual framework that retains the degraded formula estimate as the prediction anchor and learns an adaptively gated contextual correction. RASPL substantially outperforms matched direct prediction and provides stronger degradation and tail robustness than treating the formula estimate as an ordinary input feature. Within RASPL, a compact statistical encoder achieves the highest macro-averaged

R^2

and lowest computational cost, whereas a convolutional encoder achieves the strongest degradation robustness and lowest Tail95 mean absolute error (MAE). These results establish formula preservation as the central design principle for robust learning from factor-derived proxy targets.

Chayan Lahiri, Ahmed Shafee, Cody Fehringer

Department of Geosciences, Adams State University, Alamosa, Colorado, USA · Department of Computer Science, Adams State University, Alamosa, Colorado, USA · Devils Staircase Wildland Fire Module, Siuslaw National Forest, US Forest Service

Distribution Shift Robustness Residual Learning Scientific ML

Aug 4, 2026cs.LG

Physics-informed reduced-order modelling with equivariant spectral submanifolds

Spectral submanifold (SSM) reduction has emerged as a mathematically principled route to reliable nonlinear reduced-order models, capturing dynamics beyond the reach of linear techniques such as Dynamic Mode Decomposition (DMD). The computation of SSMs, however, remains computationally expensive, particularly for high-dimensional systems. In this work, we introduce equivariant spectral submanifold (eSSM) reduction, a novel extension of the SSM framework that explicitly incorporates symmetries of the full-order model into the reduction process. We establish the mathematical foundations of this approach by showing that SSMs are naturally equivariant submanifolds and that the associated charts and reduced dynamics inherit the appropriate induced group actions. Building on this framework, we develop a novel equivariant SSM reduction algorithm that exploits these symmetries to achieve substantially faster computations while also improving model robustness. We demonstrate the advantages of this approach on several benchmark problems including a test from the Common Task Framework for Science.

Georg Maierhofer

Department of Applied Mathematics and Theoretical Physics · University of Cambridge, UK

Reduced-Order Modeling Scientific ML Dimensionality Reduction

Aug 4, 2026physics.flu-dyn

TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

Yilong Dai, Yiming Sun, Yiheng Chen +4

University of Alabama Tuscaloosa, USA · University of Pittsburgh Pittsburgh, USA

Forecasting Benchmarks Scientific ML Computational Fluid Dynamics

Jul 31, 2026cs.LG

MOT-SR: Multi-Objective Tool-Augmented Scientific Equation Discovery with Large Language Models

Symbolic Regression (SR) aims to discover analytical equations from observational data and plays a central role in scientific modeling. While recent Large Language Model (LLM) based approaches show promise, they face two limitations. First, they lack data analysis mechanisms for uncovering variable dependencies, which reduces the efficiency of equation discovery. Second, most methods rely on single-objective evaluation focused solely on fitting error. This neglect of structural complexity and generalization often causes models to converge prematurely to local optima, limiting their ability to explore the broader equation space. We propose Multi-Objective Tool-augmented Symbolic Regression (MOT-SR), a unified framework that integrates external analytical tools to extract structural priors and guide equation generation, while jointly optimizing for accuracy, complexity, and generalization via a multi-objective evaluation module that maintains a dynamic Pareto front. MOT-SR employs two collaborative LLM modules: a Meta Strategy Generator, which selects tools and synthesizes structural optimization strategies based on Pareto-optimal equations, and an Equation Generator, which produces new candidate equations accordingly. The system operates in a closed-loop manner, continuously refining both strategies and equation structures. Across 40 standard tasks, MOT-SR outperforms existing SR methods in accuracy, generalization, and efficiency. We further validate MOT-SR on extreme mass-ratio inspiral (EMRI) orbital modeling, an important problem in space-based gravitational-wave astronomy where small local errors can accumulate substantially over long-term evolution. The discovered interpretable correction achieves the lowest trajectory-level integration error on held-out configurations. These results demonstrate the potential of MOT-SR to enable reliable modeling of long-horizon scientific dynamics.

Boxiao Wang, Runxiang Wang, Kai Li +4

National Key Laboratory of Cognition and Decision Intelligence for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of the Chinese Academy of Sciences, Beijing, China · School of Astronomy and Space Science, University of the Chinese Academy of Sciences, Beijing, China +2

Gravitational-Wave Astronomy Scientific ML Large Language Model-Guided Scientific Discovery Symbolic Regression

Jul 31, 2026cs.LG

DFSC: Error-Controlled Differentiable Mittag-Leffler Propagation for Fractional Scientific Machine Learning

Fractional scientific machine learning requires numerical operators that can be differentiated, batched, accelerated, and composed with neural networks. When the dominant linear fractional evolution is known through a Mittag-Leffler propagator, repeatedly reconstructing that response with a history solver or relearning it from data is unnecessary. We present DFSC, a PyTorch environment organized around the Mittag-Leffler Spectral Layer (MLSL). The layer separates known fractional propagation from data-driven corrections, so neural modules learn only unresolved dynamics while fractional orders and residual-network parameters are optimized jointly. Its adaptive algorithm increases special-function truncation depth or Lanczos dimension until successive differentiable evaluations satisfy a requested tolerance. In the negative-real alternating-series regime, DFSC additionally returns a certified first-omitted-term bound; outside that regime it explicitly labels estimates as empirical. DFSC supports dense, sparse, matrix-free, self-adjoint, generalized, and controlled complex operator paths; trainable fractional orders; direct inverse problems; residual neural composition; and CPU/GPU execution. The certified series bound covers all 59 eligible reference cases, with median bound/error effectivity 1.246 for resolved errors. Reusing a prepared batched Lanczos basis gives identical fixed-path values and reduces repeated-query time by 4.61--7.11 times on CPU and 13.07--16.22 times on an RTX 5070, excluding one-time preparation. A 27-case inverse matrix finds full-rank local curvature throughout, while remaining explicitly model-conditional. External solver and mixed real-data results support DFSC as an error-aware optional primitive for matched fractional structure, rather than a general replacement for fractional solvers or neural models.

Ning Hu, Haitao Duan, Shuqun Li +1

School of Mechanical Engineering, Hangzhou Dianzi University 1158 No. 2 Street, Qiantang District, Hangzhou 310018, China · School of Computer Science, Hangzhou Dianzi University 1158 No. 2 Street, Qiantang District, Hangzhou 310018, China · School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University 111 Ren’ai Road, Suzhou 215123, China +1

Differentiable Programming Scientific ML

Jul 30, 2026cs.CV

Physics-Aligned Self-Supervised Learning for Scientific Imaging

Data augmentations define the invariances learned by self-supervised learning (SSL). Standard augmentation pipelines were designed for natural images, yet scientific imaging modalities are governed by physical measurement processes with distinct symmetry and acquisition constraints. Enforcing invariances that contradict these constraints can distort learned representations and limit downstream performance, but practitioners moving from machine learning into a new scientific modality currently have little guidance beyond transferring natural-image pipelines unexamined. We address this gap with a principled, reproducible procedure for augmentation design in scientific SSL: we formalise the physics-aligned augmentation set as a union of measurement-consistent symmetries and acquisition-driven perturbations, and we give a concrete, largely label-free workflow---enumerate candidates, label each by the measurement operator, validate with representation-geometry diagnostics, and confirm by single-factor ablation---for selecting them. We instantiate the procedure for real-space electron microscopy and reciprocal-space 4D-STEM diffraction, and evaluate it across five SSL paradigms (DINOv2, SimCLR, MAE, VICRegL, I-JEPA) on classification and crystal-orientation regression. Physics-aligned augmentations substantially improve downstream performance for objectives relying on cross-view consistency, reduce geodesic error and improve robustness under realistic acquisition variability (detector gain, resolution loss), and systematically reshape representation geometry. While our experiments use electron microscopy, the procedure is modality-agnostic and applies to other measurement-driven domains such as medical and remote-sensing imaging. These results position augmentation design as a primary, and controllable, source of inductive bias in scientific self-supervised learning.

Bashir Kazimi, Stefan Sandfeld

Institute for Materials Data Science and Informatics (IAS-9), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany · Chair of Materials Data Science and Materials Informatics, Faculty 5 – Georesources and Materials Engineering, RWTH Aachen University, 52056, Aachen, Germany

Data Augmentation Scientific ML Self-Supervised Visual Representation Learning Microscopy Image Analysis

Jul 30, 2026hep-th

Learning to Trace Seiberg Dualities

Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order

10

), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.

Jonathan J. Heckman, Shani Meynet, Alessandro Mininno +1

Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA · Department of Physics, University of Wisconsin–Madison, 1150 University Avenue, Madison, WI 53706, USA

Transformer Scientific ML Learning-Augmented Algorithms

Jul 30, 2026cond-mat.str-el

Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets

Metallic magnets exhibit complex spin dynamics governed by electronically generated interactions. Predictive simulations of such dynamics typically require repeated solutions of an underlying electronic problem throughout the time evolution, creating a major computational bottleneck. Here we introduce a graph neural network (GNN) magnetic force-field framework that learns the effective magnetic energy functional governing itinerant spin dynamics directly from electronic calculations. Conceptually analogous to machine-learned interatomic potentials, the proposed framework enables efficient evaluation of spin torques while capturing the nonlinear and spatially extended interactions generated by itinerant electrons. We benchmark the method on representative metallic magnetic systems exhibiting collinear, noncollinear, and noncoplanar magnetic order. The learned force fields accurately reproduce electronically generated spin torques and yield nonequilibrium spin dynamics in excellent agreement with direct electronic simulations. Our results establish graph neural networks as a powerful framework for machine-learned magnetic force fields, providing a pathway toward predictive large-scale simulations of nonequilibrium magnetism across multiple length and time scales.

Ali Rayat, Yunhao Fan, Gia-Wei Chern

Department of Physics, University of Virginia, Charlottesville, VA 22904, USA

Graph Neural Networks Scientific ML Computational Materials Science

Jul 30, 2026stat.ML

On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems

We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems. It is shown that the proposed extension - that we coin as Entropy-Optimal Manifold Regression (EOMR) - allows a robust learning with linearly-scaling iteration and memory complexities. EOMR is compared to the most complete set of state-of-the-art tools from the Artificial Intelligence (AI) and Machine Learning (ML) that is available to the author, on the very challenging problems from chaotic and fluid dynamics: (i) on predicting the Lorenz-96 systems dynamics in strongly- and very-strongly chaotic regimes (with forcing parameter being

F=8

and

F=12

, respectively); and, (ii) on a data from the Hasegawa-Wakatani model on the edge of the tokamak plasma. It is demonstrated that the proposed benchmarks (i) and (ii), indeed, are the very challenging problems for the state of the art ML and AI tools - since both the general-purpose gradient boosted random forests and deep neuronal networks, as well as transformer-based AI tools like TabPFN v.03 (more spezialised for large-dimensional small data learning problems) - result in orders of magnitude inferior root mean squared prediction errors, and orders of magnitude larger model complexities, when compared to the EOMR. For a Hasegawa-Wakatani example, EOMR distills a very simple entropy-optimal and skilful description of the leading Essential Orthogonal Function (EOF) dynamics, given by linear, causal and weakly-stationary autoregressive process described by just 8 parameters.

Illia Horenko

Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.

Scientific ML Feature Selection Dimensionality Reduction Chaotic Time-Series Prediction

Jul 29, 2026cs.LG

A Lightweight Foundation Model for Collider Physics with Multi-Domain Adaptation

We present a lightweight approach to foundation modeling (\textbf{NEXUS}) that leverages pre-trained learning from collider physics data towards out-of-domain tasks in other scientific datasets, using a fully connected autoencoder model with approximately 3 million parameters. The model pre-trains with no supervision over a large-scale collision dataset from the Large Hadron Collider modeled by charged particle track features. Downstream tasks for collider analyses, such as kinematic regression and event classification, are developed on pre-trained model weights and achieve improved accuracy with only small labeled datasets when compared to equivalent architectures trained from scratch. The benefits of pre-training are additionally investigated through latent space interpretation and application to other domains, including gravitational waves, flood forecasting, and neural activity. Furthermore, the relative computational simplicity of NEXUS is demonstrated compared to transformer approaches at comparable scale, opening the door to power-efficient inference and real-time or edge applications of foundation models in scientific experiments.

Liangyu Wu, Qibin Liu, Alexander Yue +1

Department of Physics, Stanford University, 450 Jane Stanford Way, Stanford, 94305, CA, USA. · SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, 94025, CA, USA.

Self-Supervised Pre-Training High-Energy Physics Cross-Domain Transfer Learning Scientific ML

Jul 29, 2026cs.LG

From Classification to Regression: Using a Fruitfly to Solve Equations

We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data often occupy limited and recurring regions of the input space, we generate predictions by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. We apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, our offline-online workflow extracts patterns from data or governing equations during the offline phase, while online prediction requires only similarity evaluation and response aggregation. This structure helps us reduce computational and memory demands while providing explicit control over the trade-off among accuracy, storage, and inference cost.

Shady E. Ahmed, Panos Stinis

Advanced Computing, Mathematics, and Data Division Pacific Northwest National Laboratory Richland, WA 99354

Prototype-Based Learning Surrogate Modeling Nonlinear System Identification Scientific ML

Jul 26, 2026cs.LG

LAWFUL: Law-Aligned Witness for Faithful Use of Latents

When a neural network predicts a physical system accurately, has it learned the governing law as formal, structured knowledge, and if so, does the network's internal computation actually use that representation throughout the law's domain of validity? We identify four interpretability gaps that limit answering these questions for {\em physics laws over continuous variables}: the absence of a coverage-aware causal-consistency measure over continuous counterfactuals; of a domain-of-validity test for the identified circuit; of a verification of the law's invariants and forbidden behaviors; and of a quantification of how a derived physical quantity flows through the circuit. We develop a foundational framework, LAWFUL, that closes the first two and lays groundwork for the remaining two, and illustrate it on the Mocap2Radar transformer, validating whether it learns and internally uses the Doppler frequency law

f(t) = \frac{2 v(t)}λ

from motion-capture and radar data in which neither

f(t)

nor

v(t)

appears.

Kevin Chen, Kenneth W. Parker, Anish Arora

Computer Science & Engineering, The Ohio State University, Columbus, Ohio, USA · Independent Researcher, Waterford, Virginia, USA

Transformer Interpretability Mechanistic Interpretability Neural Network Interpretability Scientific ML Causal Interpretability

Jul 9, 2026cs.LG

DeepPySR -- A Symbolic Regression Framework with Dynamic Pruning, Pareto Selection, and Hierarchical Composition for Real-World Scientific Discovery

Symbolic regression (SR) discovers analytical equations from data, yielding glass-box models with directly interpretable formulas, unlike black-box methods that rely on unstable post-hoc tools such as SHAP or LIME. This transparency is crucial in clinical medicine and social science, but SR faces three challenges: high-dimensional inputs, principled selection of Pareto-front formulae, and data irregularities such as multicollinearity and class imbalance. We introduce DeepPySR, which addresses these issues with a dynamic variable-pruning schedule to remove irrelevant features during search, an exponential Pareto selection criterion that eliminates trade-offs between accuracy and complexity, and a multi-layer architecture for hierarchical symbolic composition. On four Feynman physics benchmarks and seven biomedical and social-science datasets, DeepPySR outperforms PySR and baselines on body fat (R

^2

: 0.794 vs.\ 0.702), heart disease (F1: 0.898 vs.\ 0.787), student performance (R

^2

: 0.964 vs.\ 0.948), and Raine BMI (R

^2

: 0.525 vs.\ 0.370), producing interpretable formulas aligned with domain risk factors.

Fuling Chen, Kevin Vinsen, Phillip Melton +1

International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, Perth, WA, Australia · The Raine Study, University of Western Australia, Perth, WA, Australia · Menzies Institute for Medical Research, University of Tasmania, Hobart, TAS, Australia +1

Interpretable ML Scientific ML Symbolic Regression

Jun 30, 2026cs.LG

Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression

Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing. Kernel ridge regression learning strategies are often effective when applied to clean data, but have limited success with noisy data. Recent work has observed that a weak formulation can act to filter noisy data, and different learning strategies have achieved increased noise robustness with a weak-form framework. In this manuscript, we give an overview of the filtering mechanism behind the weak formulation and provide a bias-variance error decomposition. Using these insights, we combine a weak formulation with a kernel learning strategy to propose Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems. The proposed framework is simple to implement, effective for both clean and noisy data, and outperforms several baseline methods. We demonstrate the performance of WKRR on chaotic benchmark systems in up to 64 dimensions, as well as 15,000-dimensional real-world fluid data.

Max Kreider, John Harlim, Daning Huang

Department of Mathematics The Pennsylvania State University, University Park, PA 16802, USA · Department of Mathematics, Institute for Computational and Data Sciences The Pennsylvania State University, University Park, PA 16802, USA · Department of Aerospace Engineering The Pennsylvania State University, University Park, PA 16802, USA

Kernel Ridge Regression Kernel Regression Nonlinear System Identification Chaotic Dynamical Systems Scientific ML