Model Reduction and Neural Networks

Derniers papiers

• Generalized Spherical Neural Operators: Green's Function Formulation

  Hao Tang, Hao Chen, Chao Li · 28 janvier 2026

  Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that break rotational consistency. Existing spherical operators rely…

• Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems

  Jeffrey Camlin · 28 janvier 2026

  We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method introduces a smooth monotone mapping $t \mapsto \tau(t)$ that regularizes near-singular behavior of the underlying flow while preserving its conservation laws. In the lifted coordinat…

• Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

  Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan · 28 janvier 2026

  We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form res…

• Chaotic Hedging with Iterated Integrals and Neural Networks

  Ariel Neufeld, Philipp Schmocker · 28 janvier 2026

  In this paper, we derive an $L^p$-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting the orthogonality of the expansion, we show that every $p$-integrable functional, $p \in [1,\infty)$, can be approximated…

• Out-of-Distribution Generalization for Neural Physics Solvers

  Zhao Wei, Chin Chun Ooi, Jian Cheng Wong, Abhishek Gupta, Pao-Hsiung Chiu, Yew-Soon Ong · 28 janvier 2026

  Neural physics solvers are increasingly used in scientific discovery, given their potential for rapid in silico insights into physical, materials, or biological systems and their long-time evolution. However, poor generalization beyond their training support limits exploration of novel designs and l…

• Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networks

  Kazuaki Tanaka, Kohei Yatabe · 28 janvier 2026

  The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems. However, unlike classical numerical methods that offer estab…

• SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Model

  Jan Hagnberger, Mathias Niepert · 27 janvier 2026

  Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, gen…

• SpringTime: Learning Simulatable Models of Cloth with Spatially-varying Constitutive Properties

  Guanxiong Chen, Shashwat Suri, Yuhao Wu, Yixian Cheng, Ganidhu Abeysirigoonawardena, Etienne Vouga, David I. W. Levin, Dinesh K. Pai · 27 janvier 2026

  Materials used in real clothing exhibit remarkable complexity and spatial variation due to common processes such as stitching, hemming, dyeing, printing, padding, and bonding. Simulating these materials, for instance using finite element methods, is often computationally demanding and slow. Worse, s…

• SFO: Learning PDE Operators via Spectral Filtering

  Noam Koren, Rafael Moschopoulos, Kira Radinsky, Elad Hazan · 27 janvier 2026

  Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO), a neural operator that parameterizes integral kernels using …

• Hierarchical Physics-Embedded Learning for Prediction and Discovery in Spatiotemporal Dynamical Systems

  Xizhe Wang, Xiaobin Song, Qingshan Jia, Hao Sun, Hongbo Zhao, Benben Jiang · 26 janvier 2026

  Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first principles, due to their inherent complexity, characterized b…

• Process-Tensor Tomography of SGD: Measuring Non-Markovian Memory via Back-Flow of Distinguishability

  Vasileios Sevetlidis, George Pavlidis · 26 janvier 2026

  This work proposes neural training as a \emph{process tensor}: a multi-time map that takes a sequence of controllable instruments (batch choices, augmentations, optimizer micro-steps) and returns an observable of the trained model. Building on this operational lens, we introduce a simple, model-agno…

• RONOM: Reduced-Order Neural Operator Modeling

  Sven Dummer, Dongwei Ye, Christoph Brune · 26 janvier 2026

  Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification. Reduced-order modeling (ROM) addresses these challenges by constr…

• RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation

  Dimitrios G. Patsatzis, Alessandro Della Pia, Lucia Russo, Constantinos Siettos · 22 janvier 2026

  We introduce RANDSMAPs (Random-feature/multi-scale neural decoders with Mass Preservation), numerical analysis-informed, explainable neural decoders designed to explicitly respect conservation laws when solving the challenging ill-posed pre-image problem in manifold learning. We start by proving the…

• Finite Expression Methods for Discovering Physical Laws from Data

  Zhongyi Jiang, Chunmei Wang, Haizhao Yang · 22 janvier 2026

  Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we shall present a novel deep symbolic learning method called the…

• Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators

  Yilong Dai, Shengyu Chen, Ziyi Wang, Xiaowei Jia, Yiqun Xie, Vipin Kumar, Runlong Yu · 22 janvier 2026

  Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, th…

• Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control

  Jannis Becktepe, Aleksandra Franz, Nils Thuerey, Sebastian Peitz · 22 janvier 2026

  Reinforcement learning (RL) has shown promising results in active flow control (AFC), yet progress in the field remains difficult to assess as existing studies rely on heterogeneous observation and actuation schemes, numerical setups, and evaluation protocols. Current AFC benchmarks attempt to addre…

• PDE-aware Optimizer for Physics-informed Neural Networks

  Vismay Churiwala, Hardik Shukla, Manurag Khullar · 22 janvier 2026

  Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical constraints into the loss function. However, standard optimizers such as Adam often struggle to balance competing loss terms, particularly in stiff or…

• Architecture-Optimization Co-Design for Physics-Informed Neural Networks Via Attentive Representations and Conflict-Resolved Gradients

  Pancheng Niu, Jun Guo, Qiaolin He, Yongming Chen, Yanchao Shi · 21 janvier 2026

  Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is often hindered by limited representational capacity and optimiza…

• LAViG-FLOW: Latent Autoregressive Video Generation for Fluid Flow Simulations

  Vittoria De Pellegrini, Tariq Alkhalifah · 21 janvier 2026

  Modeling and forecasting subsurface multiphase fluid flow fields underpin applications ranging from geological CO2 sequestration (GCS) operations to geothermal production. This is essential for ensuring both operational performance and long-term safety. While high fidelity multiphase simulators are …

• A universal linearized subspace refinement framework for neural networks

  Wenbo Cao, Weiwei Zhang · 21 janvier 2026

  Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace Refinement (LSR), a general and architecture-agnostic framework th…

• Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems

  Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan, Julie Bessac, Elizabeth Qian · 21 janvier 2026

  Projection-based model reduction enables efficient simulation of complex dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. The Operator Inference (OpInf) approach learns such reduced surrogate models through a two-step process: constructing a low-dimensio…

• Deep Neural networks for solving high-dimensional parabolic partial differential equations

  Wenzhong Zhang, Zhenyuan Hu, Wei Cai, George EM Karniadakis · 21 janvier 2026

  The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years, deep neural networks have emerged as a promising mesh free alte…

• Optimizing Parallel Schemes with Lyapunov Exponents and kNN-LLE Estimation

  Mudassir Shams, Andrei Velichko, Bruno Carpentieri · 21 janvier 2026

  Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contraction to oscillatory or chaotic transients depending on the choice of algorithmic parameters and initial states. A unifie…

• M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power-Law Bases

  Gnankan Landry Regis N'guessan · 21 janvier 2026

  Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner sing…

• COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates

  Benjamin Alheit, Mathias Peirlinck, Siddhant Kumar · 21 janvier 2026

  Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practic…