Physics-Informed Neural Operators

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Physics-informed neural operators learn maps from inputs such as initial conditions, parameters, or geometries to solutions of partial differential equations, so one trained model can handle many related problems. Common approaches include Fourier Neural Operators and DeepONets trained with equation-residual or weak-form losses, alongside architectures that build in properties such as conservation, incompressibility, or energy dissipation. These surrogates aim to reduce the cost of repeated simulations and the need for labeled solutions in settings such as fluid flow, phase-field evolution, Poisson problems, and elasticity. A central challenge is balancing physical fidelity and generalization against training stability and discretization mismatch: constraints can help, but may introduce bias when they do not hold for the data or resolution being modeled.

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72 papers12 papers in the last four weeks, up 20% on the four weeks before. 0.1% of all new papers.

ZENO: Nonlinear filtering with Zakai Equation Neural Operators
Oct 23, 2026Aaditya Prasad, Steven W. Flavell, Brian DePasqualeLatent Dynamics Modeling Stochastic Differential Equations
Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Howard Hughes Medical Institute, Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method
Oct 23, 2026Yuhe Wang, Zhu Wang, Min WangNeural PDE Solvers Computational Fluid Dynamics
Institute for Scientific Computation, Texas A&M University, College Station, TX 77843, USA · Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA · Department of Mathematics, University of Houston, TX 77204, USA
Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling
Oct 17, 2026Yiqiang Ye, Yichi Wang, Haodi Zhang +5Climate Downscaling Physics-Informed Neural Operators
College of Computer and Software Engineering, Shenzhen University, Shenzhen, China · School of Computer Science, Wuhan University, Wuhan, China
The importance of tensor handling and implementation of physics-informed DeepONets
Oct 15, 2026Nahum Banks, Gustavo A. M. de Almeida, Sergio MaldonadoPhysics-Informed Neural Operators PDE Operator Learning
Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK
Global-in-time Spectral Duhamel-Picard Method for Post-Exposure Bake Simulation and Physics-Informed Neural Operators for EUV Lithography
Oct 13, 2026Doyun Kim, Mircea Dusa, Werner Gilijns +1Reaction-Diffusion Systems Semiconductor Manufacturing
IMEC, Kapeldreef 75, 3001 Leuven, Belgium
Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution
Oct 10, 2026Haohan Zou, Alexander Scheinker, Yuanyuan ShiLatent Dynamics Modeling Physics-Informed Generative Modeling
University of California San Diego · Los Alamos National Laboratory
Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators
Oct 5, 2026Shilun Wei, Xiaoqiang Sun, Wei Li +1Parameter Identifiability Physics-Informed Neural Operators
School of Mathematics, Sun Yat-sen University, Guangzhou, China · School of Sciences, Great Bay University, Dongguan, China · John Hopcroft Center for Computer Science, School of Computer Science, Shanghai Jiao Tong University, Shanghai, China
Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropies
Oct 4, 2026Jason Sulskis, Sathya RaviDynamical Systems PDE Operator Learning
Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA · Also with the Georgia Tech Research Institute, Atlanta, GA, USA.
Green-Routed Neural Operators: Physics Determines Where the Network Reads
Oct 4, 2026Chenhao Si, Ming YanPDE Surrogate Modeling PDE Operator Learning
School of Data Science The Chinese University of Hong Kong, Shenzhen Shenzhen, China
PHASE: Multi-Regime Modeling of Incompressible Magnetohydrodynamics
Sep 29, 2026Radhika Achikanath Chirakkara, Rajdeep Haldar, Zezheng Song +1Magnetohydrodynamics PDE Operator Learning
Canadian Institute for Theoretical Astrophysics, University of Toronto, ON, Canada, M5S 3H8 · Department of Statistics, Purdue University, IN, United States of America, 47907 · University of Maryland, College Park, MD, United States of America, 20742 +1
Preconditioned Physics-Informed Neural Operator Training
Sep 28, 2026Shizheng Wen, Siddhartha Mishra, Marius ZeinhoferPhysics-Informed Neural Operators PDE Operator Learning
ETH Zürich
KernelOnet: An Interpretable Neural Operator Based on Kernel Functions
Sep 28, 2026Yuan Guo, Hanshu Chen, Qiang Xi +2PDE Operator Learning Neural Operators
College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, China · Institute of Structural Mechanics, Bauhaus-University Weimar, Weimar 99423, Germany · Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University, Nanjing 210098, China
When Known Physics Helps Neural PDE Models: Residual Constraints Out-Regularize Generic Priors for Nonlinear Dynamics
Sep 27, 2026Zahra Farazpay, Aniruddha BoraPDE Surrogate Modeling Physics-Informed ML
Department of Physics Louisiana Tech University Ruston, LA, USA · Department of Computer Science Texas State University San Marcos, TX, USA
Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency
Sep 26, 2026Xinhan Yang, Lu Lu, Shancong MouNeural Operators Physics-Informed Neural Operators
Department of Industrial and Systems Engineering, University of Minnesota Minneapolis, MN 55455 · Department of Statistics and Data Science, Yale University New Haven, CT 06511, USA
Physics and Data Driven Transformer-Mamba Framework for Flow Field
Sep 24, 2026Zhuo Zhang, Shun Zou, Canqun Yang +1PDE Surrogate Modeling PDE Operator Learning
College of Computer Science and Technology, National University of Defense Technology, Changsha, China · College of Artificial Intelligence, Nanjing Agricultural University, NanJing, China · National SuperComputer Center in Tianjin, Binhai New Area, Tianjin, China +1
Learning Physics from an Imperfect Ancestor
Sep 21, 2026S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas +1PDE Surrogate Modeling OOD Generalization
Sibley School of Mechanical and Aerospace Engineering, Cornell University · AI Lab, Siemens Energy · Department of Civil and Systems Engineering, Johns Hopkins University
A Physics-Conditioned Neural Operator for Generalization of Atrioventricular Valve Mechanics across Pressure and Tissue Properties
Sep 20, 2026Shawn Koohy, Wensi Wu, Matthew A Jolley +1Surrogate Modeling Physics-Informed Neural Operators
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA. · Cardiovascular Institute, Children’s Hospital of Philadelphia, Philadelphia, PA, USA. · Department of Anesthesiology and Critical Care Medicine, Children’s Hospital of Philadelphia, Philadelphia, PA, USA. +1
A Data-Free Physics-Informed Neural Operator for Level-Set Interface Advection
Sep 18, 2026Muhammad Akbar KhanPDE Operator Learning Physics-Informed Neural Operators
Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan
Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transport
Sep 14, 2026Zixuan Shen, Quanxu Wan, Bingchuan Wang +2Adaptive Mesh Refinement Physics-Informed Neural Operators
Central South University · Nanjing University
Enhancing generalization in endwall film cooling prediction: Incorporating the superposition principle into transformer-based neural operators
Sep 10, 2026Qineng Wang, Liming Song, Tianyuan Liu +1Transformer Neural Operator Neural Network Generalization
Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China · ENN Science and Technology Development China Co., Ltd., Langfang, Hebei, 065001, China · Hebei Key Laboratory of Compact Fusion, Langfang, Hebei, 065001, China
Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures
Sep 3, 2026Amar Alem Koric, Qibang Liu, Seid KoricPDE Operator Learning Deep Operator Networks
Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA · National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 1205 W. Clark St., Urbana, IL, 61801, USA · The Grainger College of Engineering, Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL, 61801, USA
GenONet: A Generative operator Network for High-Resolution Precipitation Nowcasting
Sep 1, 2026Mohammad Kian Golkar, Luciano Alves de Oliveira, Mohammad KhanjaniPrecipitation Forecasting Spatiotemporal Forecasting
University of Illinois Urbana-Champaign · Sharif University of Technology
A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamics
Aug 26, 2026Wenpu Du, Peng Zhou, Yunlong Xia +5PDE Operator Learning Physics-Informed Neural Operators
School of Environment and Safety Engineering, North University of China, Taiyuan, 030051, China
Physics-Integrated Operator Learning via Gaussian Splatting Representations
Aug 25, 2026Jihao Zhang, Junyi Guo, Jian-Xun WangPDE Operator Learning PDE Surrogate Modeling
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA
Physics-Unrolled Neural Operator for Wireless Field Modeling
Aug 19, 2026Rafid Umayer Murshed, Saif Ur Rahman, Mingyue Tang +1Radio Propagation Modeling Physics-Informed Neural Operators
Department of Computer Science University of Illinois Urbana-Champaign Urbana, IL 61801, USA
DeepOHeat-v2: Self-Improving Operator Learning for Fast and Trustworthy Thermal Optimization in 3D-IC Design
Aug 17, 2026Xinling Yu, Yixing Li, Ziyue Liu +4PDE Operator Learning Surrogate-Assisted Optimization
Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106 USA · Cadence Design Systems, Austin, TX 78759 USA · Department of Computer Science, University of California, Santa Barbara, CA 93106 USA +1
Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets
Aug 13, 2026Oscar L. Cruz-Gonzalez, Valérie Deplano, Badih GhattasDeep Operator Networks Physics-Informed Neural Operators
Aix Marseille Univ, CNRS, AMSE UMR 7316, Marseille, France · Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France
HIPNO: Symmetry-Aware Physics-Informed Neural Operators for Noninvasive Hemodynamic Inference
Aug 8, 2026Yunbei Pan, Jiahang Sha, Simon A. Lee +3Physics-Informed Neural Operators
Department of Computational Medicine, UCLA · Scalable Analytics Institute (ScAi), Department of Computer Science, UCLA · Department of Anesthesiology & Perioperative Medicine, UCLA +1
A Physics-Informed Hybrid Neural Operator for Transient Magnetization Prediction in Power Magnetics
Aug 3, 2026Yachao Zhu, Qiujie Huang, Sinan Li +3Materials Property Prediction Physics-Informed Neural Operators
School of Electrical and Computer Engineering, the University of Sydney, Darlington, NSW, 2008, Australia · National Railway Research and Design Institute of Signal and Communication, Beijing 100070, China
SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics
Jul 28, 2026Shivani Saini, Ramesh Kumar Vats, Arup Kumar SahooStructural Mechanics PDE Operator Learning
Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur, 177005, Himachal Pradesh, India · The Hatter Department of Marine Technologies, Leon H. Charney School of Marine Sciences, University of Haifa, 3498838, Haifa, Israel

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ZENO: Nonlinear filtering with Zakai Equation Neural Operators

Aaditya Prasad, Steven W. Flavell, Brian DePasquale

Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Howard Hughes Medical Institute, Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA

Latent Dynamics Modeling Stochastic Differential Equations Physics-Informed Neural Operators

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State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai equation, a stochastic partial differential equation (SPDE) that combines the forward Kolmogorov operator (known as the Fokker-Planck equation) with observed likelihood updates. Although solving these high-dimensional SPDEs is often impossible analytically and intractable numerically, advances in operator learning and physics-informed machine learning have made it feasible. Harnessing these advances, we introduce the Zakai Equation Neural Operator (ZENO), a model that optimizes a neural operator against a Zakai Equation based physics-informed loss to approximate the exact unnormalized filtering distribution for latent stochastic dynamical systems. We use this ZENO-inferred posterior distribution in an expectation-maximization (EM) framework to perform parameter learning and state inference. We demonstrate ZENO's ability to accurately infer the posterior distribution and learn its corresponding SDE parameters in three simulated stochastic dynamical systems (Double-Well bistable system, Van Der Pol (VDP) oscillator, and Lorenz system) and compare its performance against established methods for latent SDE inference and learning. We show that ZENO recovers previously observed limit cycles representing forward and backward locomotion from a whole-brain imaging dataset of immobilized C. elegans nematodes. ZENO is a novel approach to the problem of nonlinear filtering and dynamical inference through the lens of partial differential equations and operator theory.