Model Reduction and Neural Networks

Derniers papiers

• Goal-oriented learning of stochastic differential equations using error bounds on path-space observables

  Joanna Zou, Han Cheng Lie, Youssef Marzouk · 2 juillet 2026

  Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties. Surrogate models of the drift function of an SDE, learned …

• Generative Model Proposal based Particle Filtering for Data Assimilation

  Chandni Nagda, Mayank Shrivastavam Gudrun Thorkelsdottir, Gan Zhang, Morteza Mardani, Arindam Banerjee · 2 juillet 2026

  Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications. In the filtering setting, the goal is to model the posterior over the current state given all observations so far. Classical solutions typically make simplifying distribution…

• Learning Cardiac Motion Priors for Implicit Neural Representations

  Andrew Bell, George Webber, Andrew P King, Steffen E Petersen, Muhummad Sohaib Nazir, Alistair Young · 2 juillet 2026

  Implicit neural representations (INRs) are well suited to cardiac motion estimation, providing continuous, compact representations of motion fields. However, fitting an INR to each image sequence is time-consuming and sensitive to the optimisation trajectory. Learned priors can help guide optimisati…

• GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems

  Meenakshi Krishnan, Pranav Pulijala, Ke Chen, Haizhao Yang, Ramani Duraiswami · 2 juillet 2026

  Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. Although recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs s…

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

  Max Kreider, John Harlim, Daning Huang · 2 juillet 2026

  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…

• From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators

  Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek · 2 juillet 2026

  We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficiently approximate and learn solution operators whenever these operators admit stabl…

• TRIE: An Evaluation Framework for Stochastic PDE Surrogates

  Bharat Srikishan, Javier E. Santos, Nikhil Muralidhar, Charles D. Young · 2 juillet 2026

  Many scientific systems exhibit uncertainty from stochastic forcing, unresolved degrees of freedom, or imperfect observations, making reliable surrogate forecasting fundamentally distributional rather than pointwise. For such systems, deterministic neural surrogates fail to capture statistical measu…

• GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics

  Jeffrey Fang, Keyi Shen, Anutam Srinivasan, Glen Chou · 2 juillet 2026

  This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, differentiable, GPU-parallel …

• A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

  Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang · 2 juillet 2026

  Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters. An effective approach to address thes…

• Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification

  Onkar Jadhav, Tim French, Matthew Rayson, Nicole L. Jones · 1 juillet 2026

  Diffusion models enable probabilistic super-resolution and conditional generation, but pixel-space methods are computationally expensive and learned latent spaces often lack interpretable uncertainty quantification. We introduce Patch-PODiff-ViT, a structured latent diffusion framework in which the …

• A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements

  Kundan Kumar, Shreya Das, Simo S\"arkk\"a · 1 juillet 2026

  This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies …

• Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias

  Yujin Kim, Nidhi Soma, Sarah Dean · 1 juillet 2026

  Probabilistic downscaling is the task of modeling the conditional distribution of high-resolution fields given coarse inputs, and is a central challenge to atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic…

• The HydroGym Reinforcement Learning Platform for Fluid Dynamics

  Christian Lagemann, Sajeda Mokbel, Miro Gondrum, Mario R\"uttgers, Yuning Wang, Pol Su\'arez, Ludger Paehler, Deniz A. Bezgin, Aaron B. Buhendwa, Jared L. Callaham, Samuel Ahnert, Nicholas Zolman, Xiao Shao, Jean-Christophe Loiseau, Nikolaus Adams, Matthias Meinke, Wolfgang Schr\"oder, Kai Lagemann, Esther Lagemann, Ricardo Vinuesa, Steven L. Brunton · 1 juillet 2026

  Modeling and controlling fluids is critical across science and engineering. Effective flow control can increase lift, reduce drag, enhance mixing, and attenuate noise, potentially unlocking new technologies. Yet controlling fluids is hard: the dynamics are high-dimensional, nonlinear, and multiscale…

• Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains

  Haixin Wang, Haoning Dang, Fei Wang, Shimin Guo · 1 juillet 2026

  Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods often require problem-dependent artificial boundary conditions, while global spectral bases may be inefficient for localize…

• Offline Reinforcement Learning for Fluid Controls: Data-based Multi-observational Policy Extraction

  Deepak Akhare, Luning Sun, Xin-Yang Liu, Xiantao Fan, Timo Bremer, Ben Zhu, Jian-Xun Wang · 1 juillet 2026

  Active flow control is a fundamental application in engineering. Recent advances in deep reinforcement learning have made progress in this field. However, the classical online RL approaches require extensive real-time interactions with the high fidelity environment, while each sensor configuration c…

• Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization

  Hao Xu, Siyu Lou, Yuntian Chen, Dongxiao Zhang · 1 juillet 2026

  Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning. Current data-driven approaches typically operate on a single dataset, inherently limiting their performance when faced with restricted observations. In practice, multiple…

• Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment

  Jason Sulskis, Sathya Ravi · 1 juillet 2026

  Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neura…

• Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

  Yi Zhang, Peng Wang, Difan Zou · 30 juin 2026

  Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems. Recently, diffusion models have gained increasing attention in the modeling of physical systems…

• Entropy-Regularized Reinforcement Learning for Linear-Quadratic Stackelberg Differential Games in Regime-Switching Diffusion Models

  Congde Hu, Danping Li, Lin Xu, Wenying Xu · 30 juin 2026

  Stackelberg differential games (SDGs) provide a powerful framework for hierarchical decision-making in stochastic and continuous-time environments, yet their solution remains computationally challenging due to the complexity of traditional dynamic programming and Hamilton-Jacobi-Bellman-Isaacs (HJBI…

• Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation

  George Coote, Matthew J. Colbrook · 30 juin 2026

  Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust. A finite EDMD matrix always has eigenvalues; the problem is that many of them may have nothing to do with the infinite-dimensional operator. In this paper we make spec…

• Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps

  Chenhui Zhu, Fei Wang · 30 juin 2026

  We study operator learning for random obstacle-to-solution maps arising from elliptic variational inequalities with finite-band self-affine random obstacle fields. Instead of introducing an explicit truncated stochastic parametrization of the random input, we learn the map directly from sampled obst…

• PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation

  Yihan Zhang, Zhiteng Zhang, Kun Chen, Chen Wang · 30 juin 2026

  Technology computer-aided design (TCAD) semiconductor device simulation is fundamentally constrained by the high computational cost of iteratively solving coupled drift-diffusion equations. Existing ML surrogates either reduce internal physics to macroscopic scalar regressions, or rely on single-ste…

• Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures

  L. U. Abdullaev, F. Herrera, U. A. Rozikov, M. V. Velasco · 30 juin 2026

  We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interac…

• A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification

  Geoffrey Davis, Ashwin Renganathan · 30 juin 2026

  Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experim…

• Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

  Raul Jimenez, David Mateos, Pavlos Protopapas, Pau Sol\'e-Vilar\'o, Pedro Taranc\'on-\'Alvarez, Pablo Tejerina-P\'erez · 30 juin 2026

  We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormaliza…