Model Reduction and Neural Networks

Derniers papiers

• Physics-informed neural network for predicting fatigue life of unirradiated and irradiated austenitic and ferritic/martensitic steels under reactor-relevant conditions

  Dhiraj S Kori, Abhinav Chandraker, Syed Abdur Rahman, Punit Rathore, Ankur Chauhan · 20 mars 2026

  This study proposes a Physics-Informed Neural Network (PINN) framework to predict the low-cycle fatigue (LCF) life of irradiated austenitic and ferritic/martensitic (F/M) steels used in nuclear reactors. These materials undergo cyclic loading, neutron irradiation, and elevated temperatures, leading …

• A Family of Adaptive Activation Functions for Mitigating Failure Modes in Physics-Informed Neural Networks

  Krishna Murari · 20 mars 2026

  Physics-Informed Neural Networks(PINNs) are a powerful and flexible learning framework that has gained significant attention in recent years. It has demonstrated strong performance across a wide range of scientific and engineering problems. In parallel, wavelets have been extensively used as efficie…

• Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models

  Riccardo Saporiti, Fabio Nobile · 20 mars 2026

  We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution, parametrically with respect to the location of the initial mass. By u…

• Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations

  Hongjue Zhao, Yizhuo Chen, Yuchen Wang, Hairong Qi, Lui Sha, Tarek Abdelzaher, Huajie Shao · 20 mars 2026

  Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a theoretical foundation for understanding, analyzing, and improving D…

• Physically Accurate Differentiable Inverse Rendering for Radio Frequency Digital Twin

  Xingyu Chen, Xinyu Zhang, Kai Zheng, Xinmin Fang, Tzu-Mao Li, Chris Xiaoxuan Lu, Zhengxiong Li · 20 mars 2026

  Digital twins, virtual simulated replicas of physical scenes, are transforming system design across industries. However, their potential in radio frequency (RF) systems has been limited by the non-differentiable nature of conventional RF simulators. The visibility of propagation paths causes severe …

• Learning Transferable Friction Models and LuGre Identification Via Physics-Informed Neural Networks

  Asutay Ozmen, Jo\~ao P. Hespanha, Katie Byl · 20 mars 2026

  Accurately modeling friction in robotics remains a core challenge, as robotics simulators like MuJoCo and PyBullet use simplified friction models or heuristics to balance computational efficiency with accuracy, where these simplifications and approximations can lead to substantial differences betwee…

• Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach

  Rahul Halder, Arash Hajisharifi, Kabir Bakhshaei, Gianluigi Rozza · 20 mars 2026

  We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D Computational Fluid Dynamics (CFD) snapshots of an idealised basilar …

• Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

  Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fern\'andez, Jun Liu · 20 mars 2026

  Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physics-informed neural networks fundamentally depart from this paradigm: they approximate solutions by minimizing residual l…

• A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials

  Purna Vindhya Kota, Meer Mehran Rashid, Somdatta Goswami, Lori Graham-Brady · 20 mars 2026

  Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to o…

• Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training

  Wenshuo Wang, Fan Zhang · 20 mars 2026

  Researchers train neural simulators on uniformly sampled numerical simulation data. But under the same budget, does systematically sampled data provide the most effective information? A fundamental yet unformalized problem is how to sample training data for neural simulators so as to maximize rollou…

• SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

  Amanda A. Howard, Nicholas Zolman, Bruno Jacob, Steven L. Brunton, Panos Stinis · 20 mars 2026

  Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complemen…

• Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems

  Qi Liu, Laure Zanna, Joan Bruna · 19 mars 2026

  Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in autoregressive rollouts that severely degrade generation quality over l…

• JAWS: Enhancing Long-term Rollout of Neural PDE Solvers via Spatially-Adaptive Jacobian Regularization

  Fengxiang Nie, Yasuhiro Suzuki · 19 mars 2026

  Data-driven surrogate models can significantly accelerate the simulation of continuous dynamical systems, yet the step-wise accumulation of errors during autoregressive time-stepping often leads to spectral blow-up and unphysical divergence. Existing global regularization techniques can enforce cont…

• Translation Invariance of Neural Operators for the FitzHugh-Nagumo Model

  Luca Pellegrini · 19 mars 2026

  Neural Operators (NOs) are a powerful deep learning framework designed to learn the solution operator that arise from partial differential equations. This study investigates NOs ability to capture the stiff spatio-temporal dynamics of the FitzHugh-Nagumo model, which describes excitable cells. A key…

• Neural Pushforward Samplers for the Fokker-Planck Equation on Embedded Riemannian Manifolds

  Andrew Qing He, Wei Cai · 19 mars 2026

  In this paper, we extend the Weak Adversarial Neural Pushforward Method to the Fokker--Planck equation on compact embedded Riemannian manifolds. The method represents the solution as a probability distribution via a neural pushforward map that is constrained to the manifold by a retraction layer, en…

• RHYME-XT: A Neural Operator for Spatiotemporal Control Systems

  Marijn Ruiter, Miguel Aguiar, Jake Rap, Karl H. Johansson, Amritam Das · 19 mars 2026

  We propose RHYME-XT, an operator-learning framework for surrogate modeling of spatiotemporal control systems governed by input-affine nonlinear partial integro-differential equations (PIDEs) with localized rhythmic behavior. RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional…

• Interpretable AI-Assisted Early Reliability Prediction for a Two-Parameter Parallel Root-Finding Scheme

  Bruno Carpentieri, Andrei Velichko, Mudassir Shams, Paola Lecca · 19 mars 2026

  We propose an interpretable AI-assisted reliability diagnostic framework for parameterized root-finding schemes based on kNN-LLE proxy stability profiling and multi-horizon early prediction. The approach augments a numerical solver with a lightweight predictive layer that estimates solver reliabilit…

• Verification and Validation of Physics-Informed Surrogate Component Models for Dynamic Power-System Simulation

  Petros Ellinas, Indrajit Chaudhuri, Johanna Vorwerk, Spyros Chatzivasileiadis · 19 mars 2026

  Physics-informed machine learning surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. The key question, however, is not only whether a surrogate matches a stand-alone component model on average, but whether it remains accu…

• Trajectory-Optimized Time Reparameterization for Learning-Compatible Reduced-Order Modeling of Stiff Dynamical Systems

  Joe Standridge, Daniel Livescu, Paul Cizmas · 19 mars 2026

  Stiff dynamical systems present a challenge for machine-learning reduced-order models (ML-ROMs), as explicit time integration becomes unstable in stiff regimes while implicit integration within learning loops is computationally expensive and often degrades training efficiency. Time reparameterizatio…

• PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturing

  Benjamin Uhrich, Tim H\"antschel, Erhard Rahm · 17 mars 2026

  A comprehensive understanding of heat transport is essential for optimizing various mechanical and engineering applications, including 3D printing. Recent advances in machine learning, combined with physics-based models, have enabled a powerful fusion of numerical methods and data-driven algorithms.…

• Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention

  Markus W. Baumgartner, Anson Lei, Joe Watson, Ingmar Posner · 17 mars 2026

  Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of candidate functions chosen via available domain knowledge. In c…

• Neural Networks as Local-to-Global Computations

  Vicente Bosca, Robert Ghrist · 17 mars 2026

  We construct a cellular sheaf from any feedforward ReLU neural network by placing one vertex for each intermediate quantity in the forward pass and encoding each computational step - affine transformation, activation, output - as a restriction map on an edge. The restricted coboundary operator on th…

• Building Trust in PINNs: Error Estimation through Finite Difference Methods

  Aleksander Krasowski, Ren\'e P. Klausen, Aycan Celik, Sebastian Lapuschkin, Wojciech Samek, Jonas Naujoks · 17 mars 2026

  Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their flexibility, PINNs offer limited insight into how their predictions…

• A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM)

  Emil Hovad · 17 mars 2026

  We introduce a Stability-Aware Frozen Euler autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM) that recovers material parameters and temporal field evolution from videos of physical processes. The architecture is an autoencoder whose latent-space transition is governed by…

• Data-driven Progressive Discovery of Physical Laws

  Mingkun Xia, Weiwei Zhang · 17 mars 2026

  Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step" process, which often generates lengthy and physically meaningless…