Model Reduction and Neural Networks

Derniers papiers

• Unsupervised simulation of incompressible flows with physics- and equality- constrained artificial neural networks

  Qifeng Hu, Inanc Senocak · 15 mai 2026

  Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations, yet their success in simulating incompressible flows at high Reynolds numbers remains limited. Existing approaches rely on auxiliary labeled data, supervised pretraining, or reference solutions, a…

• When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability

  ML Nissen Gonzalez, Melwina Albuquerque, Laurence Wroe, Jacob Meyer Cohen, Logan Riggs Smith, Thomas Dooms · 15 mai 2026

  Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent paramete…

• Eradicating Negative Transfer in Multi-Physics Foundation Models via Sparse Mixture-of-Experts Routing

  Ellwil Sharma, Arastu Sharma · 15 mai 2026

  Scaling Scientific Machine Learning (SciML) toward universal foundation models is bottlenecked by negative transfer: the simultaneous co-training of disparate partial differential equation (PDE) regimes can induce gradient conflict, unstable optimization, and plasticity loss in dense neural operator…

• Discovering Physical Directions in Weight Space: Composing Neural PDE Experts

  Pengkai Wang, Pengwei Liu, Yuanyi Wang, Guanyu Chen, Xingyu Ren, Xiaolong Li, Zhongkai Hao, Yuting Kong, Qixin Zhang, Dong Ni · 15 mai 2026

  Recent advances in neural operators have made partial differential equation (PDE) surrogate modeling increasingly scalable and transferable through large-scale pretraining and in-context adaptation. However, after a shared operator is fine-tuned to multiple regimes within a continuous physical famil…

• Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks

  Ryoichiro Agata, Tomohisa Okazaki · 15 mai 2026

  Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically me…

• MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration

  Qiyun Cheng, Md Hossain Sahadath, Huihua Yang, Shaowu Pan, Wei Ji · 15 mai 2026

  The computational overhead of traditional numerical solvers for partial differential equations (PDEs) remains a critical bottleneck for large-scale parametric studies and design optimization. We introduce a Minimal-Data Parametric Neural Operator Preconditioning (MD-PNOP) framework, which establishe…

• Unbiased and Second-Order-Free Training for High-Dimensional PDEs

  Jaemin Seo, Surin Lee, Jae Yong Lee · 15 mai 2026

  Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can …

• A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures

  Sergio Vanegas, Lasse Lensu, Fredy Ruiz · 15 mai 2026

  Building black-box models for dynamical systems from data is a challenging problem in machine learning, especially when asymptotic stability guarantees are required. In this paper, we introduce a novel stability-ensuring and backpropagation-compatible projection scheme based on the Schur decompositi…

• Watch your neighbors: Training statistically accurate chaotic systems with local phase space information

  Joon-Hyuk Ko, Andrus Giraldo, Deok-Sun Lee · 15 mai 2026

  Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a good surrogate model for chaotic dynamics is. Prior work has …

• MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

  Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Serafim Kalliadasis · 14 mai 2026

  Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum…

• Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation

  Runlong Xie, An Luo · 14 mai 2026

  Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations. While recent neural operator architectures have demonstrated s…

• Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction

  Florian Hess, Florian G\"otz, Daniel Durstewitz · 14 mai 2026

  Reconstructing nonlinear dynamical systems (DS) from data (DSR) is a fundamental challenge in science and engineering, but it inherently relies on sequential models. Recent breakthroughs for sequential models have produced algorithms that parallelize computation along sequence length $T$, achieving …

• Identifying the nonlinear string dynamics with port-Hamiltonian neural networks

  Maximino Linares, Guillaume Doras, Thomas H\'elie · 14 mai 2026

  Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open, non-autonomous dynamical systems, have been successfully integrated with …

• Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems

  Dengfei Zeng, Lijian Jiang, Shuyu Sun, Dunhui Xiao · 14 mai 2026

  A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between t…

• Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations

  Phillip Si, Yuan Qiu, Omar Sallam, Jeremy Feinstein, Ziang He, Eugene Yan, Peng Chen · 14 mai 2026

  AI-driven flood digital twins demand fast hydrodynamic surrogates for ensemble forecasting and observation assimilation. Yet even GPU-accelerated two-dimensional shallow water equation (SWE) solvers still require $\sim 55$ minutes per $96$-hour run on a $\sim 4.2$-million-active-cell metropolitan ba…

• Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations

  Zhonghao Li, Chaoyu Liu, Qian Zhang · 14 mai 2026

  Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both classical numerical solvers and existing neural approaches. Wh…

• Unified generalization analysis for physics informed neural networks

  Yuka Hashimoto, Tomoharu Iwata · 14 mai 2026

  Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems. Existing generalization analyses for PINNs and VPINNs remain limited, often requiring restrictive assumptions such as s…

• U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics

  Yingzhe Ma, Xiao Yang, Yuxin Xie, Zihan Xiong, Jinliang Liu · 14 mai 2026

  Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of slowly varying backgrounds. This poses a challenge for neur…

• Mixed neural posterior estimation for simulators with discrete and continuous parameters

  Jan Boelts, Cornelius Schr\"oder, Jonas Beck, Jakob H. Macke, Michael Deistler, Daniel Gedon · 14 mai 2026

  Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be \emph{continuous}. However, many scientific models involve pa…

• Topology-Preserving Neural Operator Learning via Hodge Decomposition

  Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette · 14 mai 2026

  In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, ena…

• Local Inverse Geometry Can Be Amortized

  Aaditya L. Kachhadiya · 14 mai 2026

  Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based linearized systems. We propose a learned alternative: amortize local …

• Hierarchical Transformer Preconditioning for Interactive Physics Simulation

  Carl Osborne, Minghao Guo, Crystal Owens, Wojciech Matusik · 14 mai 2026

  Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We introduce the Hierarchical Transformer Preconditioner, a neura…

• Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks

  Lingfei Kong, Haoran Ma · 14 mai 2026

  This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-v…

• A PDE Perspective on Generative Diffusion Models

  Kang Liu, Enrique Zuazua · 13 mai 2026

  Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only partially understood, particularly regarding the stability and…

• Steerable Neural ODEs on Homogeneous Spaces

  Emma Andersdotter, Daniel Persson, Fredrik Ohlsson · 13 mai 2026

  We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature vectors transforming under the local symmetry group $H$. We in…