Model Reduction and Neural Networks

Derniers papiers

• A Multiplicative Neural Network Architecture: Locality and Regularity of Appriximation

  Hee-Sun Choi, Beom-Seok Han · 9 février 2026

  We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal approximation theorem for this architecture and analyze its appro…

• Memory-Conditioned Flow-Matching for Stable Autoregressive PDE Rollouts

  Victor Armegioiu · 9 février 2026

  Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffusion and flow-matching generators: although their internal dynamics are Markovian…

• Learning Deep Hybrid Models with Sharpness-Aware Minimization

  Naoya Takeishi · 9 février 2026

  Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, effectively the scientific models may be ignored in prediction due to the flexibility of the machine learning mod…

• Diffeomorphism-Equivariant Neural Networks

  Josephine Elisabeth Oettinger, Zakhar Shumaylov, Johannes Bostelmann, Jan Lellmann, Carola-Bibiane Sch\"onlieb · 9 février 2026

  Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimen…

• Physics-informed extreme learning machine for Terzaghi consolidation problems and interpretation of coefficient of consolidation based on CPTu data

  He Yang, Pin-Qiang Mo, Fei Ren, Hai-Sui Yu, Xueyu Geng, Pei-Zhi Zhuang · 9 février 2026

  This paper conducts a preliminary study to investigate the feasibility of a physics-informed extreme learning machine (PIELM) for solving the Terzaghi consolidation equation and interpreting the coefficient of consolidation of soil from piezocone penetration tests (CPTu). In the PIELM framework, the…

• Toward generative machine learning for boosting ensembles of climate simulations

  Parsa Gooya, Reinel Sospedra-Alfonso, Johannes Exenberger · 9 février 2026

  Accurately quantifying uncertainty in predictions and projections arising from irreducible internal climate variability is critical for informed decision making. Such uncertainty is typically assessed using ensembles produced with physics based climate models. However, computational constraints impo…

• Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter

  Yuhan Wu, Jan Willem van Beek, Victorita Dolean, Alexander Heinlein · 9 février 2026

  Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence. Despite this promise, many DL-HIMs stagnate at false fixed points where neural updates vanish while the physica…

• Inference-Time Rethinking with Latent Thought Vectors for Math Reasoning

  Deqian Kong, Minglu Zhao, Aoyang Qin, Bo Pang, Chenxin Tao, David Hartmann, Edouardo Honig, Dehong Xu, Amit Kumar, Matt Sarte, Chuan Li, Jianwen Xie, Ying Nian Wu · 9 février 2026

  Standard chain-of-thought reasoning generates a solution in a single forward pass, committing irrevocably to each token and lacking a mechanism to recover from early errors. We introduce Inference-Time Rethinking, a generative framework that enables iterative self-correction by decoupling declarativ…

• Position: Universal Time Series Foundation Models Rest on a Category Error

  Xilin Dai, Wanxu Cai, Zhijian Xu, Qiang Xu · 6 février 2026

  This position paper argues that the pursuit of "Universal Foundation Models for Time Series" rests on a fundamental category error, mistaking a structural Container for a semantic Modality. We contend that because time series hold incompatible generative processes (e.g., finance vs. fluid dynamics),…

• Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models

  Freja H{\o}gholm Petersen, Jesper Sandvig Mariegaard, Rocco Palmitessa, Allan P. Engsig-Karup · 6 février 2026

  While POD-based surrogates are widely explored for hydrodynamic applications, the use of Koopman Autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary con…

• Visualizing the loss landscapes of physics-informed neural networks

  Conor Rowan, Finn Murphy-Blanchard · 6 février 2026

  Training a neural network requires navigating a high-dimensional, non-convex loss surface to find parameters that minimize this loss. In many ways, it is surprising that optimizers such as stochastic gradient descent and ADAM can reliably locate minima which perform well on both the training and tes…

• Provably Reliable Classifier Guidance via Cross-Entropy Control

  Sharan Sahu, Arisina Banerjee, Yuchen Wu · 6 février 2026

  Classifier-guided diffusion models generate conditional samples by augmenting the reverse-time score with the gradient of the log-probability predicted by a probabilistic classifier. In practice, this classifier is usually obtained by minimizing an empirical loss function. While existing statistical…

• Progressive multi-fidelity learning with neural networks for physical system predictions

  Paolo Conti, Mengwu Guo, Attilio Frangi, Andrea Manzoni · 6 février 2026

  Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and in real-time. Even building sufficiently accurate surrogate m…

• Logical Guidance for the Exact Composition of Diffusion Models

  Francesco Alesiani, Jonathan Warrell, Tanja Bien, Henrik Christiansen, Matheus Ferraz, Mathias Niepert · 6 février 2026

  We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas ca…

• Symplectic convolutional neural networks

  S\"uleyman Y{\i}ld{\i}z, Konrad Janik, Peter Benner · 6 février 2026

  We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form of the convolution layer and then, using symplectic neural n…

• SpectraKAN: Conditioning Spectral Operators

  Chun-Wun Cheng, Carola-Bibiane Sch\"onlieb, Angelica I. Aviles-Rivero · 6 février 2026

  Spectral neural operators, particularly Fourier Neural Operators (FNO), are a powerful framework for learning solution operators of partial differential equations (PDEs) due to their efficient global mixing in the frequency domain. However, existing spectral operators rely on static Fourier kernels …

• Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithm

  Shizheng Wen, Mingyuan Chi, Tianwei Yu, Ben Moseley, Mike Yan Michelis, Pu Ren, Hao Sun, Siddhartha Mishra · 6 février 2026

  We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying variational forms, and its high efficiency stems from a novel hig…

• Smoothness Errors in Dynamics Models and How to Avoid Them

  Edward Berman, Luisa Li, Jung Yeon Park, Robin Walters · 6 février 2026

  Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly s…

• Imposing Boundary Conditions on Neural Operators via Learned Function Extensions

  Sepehr Mousavi, Siddhartha Mishra, Laura De Lorenzis · 6 février 2026

  Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to bou…

• Structural Disentanglement in Bilinear MLPs via Architectural Inductive Bias

  Ojasva Nema, Kaustubh Sharma, Aditya Chauhan, Parikshit Pareek · 6 février 2026

  Selective unlearning and long-horizon extrapolation remain fragile in modern neural networks, even when tasks have underlying algebraic structure. In this work, we argue that these failures arise not solely from optimization or unlearning algorithms, but from how models structure their internal repr…

• Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries

  Hang Zhou, Haixu Wu, Haonan Shangguan, Yuezhou Ma, Huikun Weng, Jianmin Wang, Mingsheng Long · 6 février 2026

  Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells remains a fundamental challenge due to the prohibitive memo…

• Causal explanations of outliers in systems with lagged time-dependencies

  Philipp Alexander Schwarz, Johannes Oberpriller, Sven Klaassen · 5 février 2026

  Root-cause analysis in controlled time dependent systems poses a major challenge in applications. Especially energy systems are difficult to handle as they exhibit instantaneous as well as delayed effects and if equipped with storage, do have a memory. In this paper we adapt the causal root-cause an…

• Jacobian Regularization Stabilizes Long-Term Integration of Neural Differential Equations

  Maya Janvier, Julien Salomon, Etienne Meunier · 5 février 2026

  Hybrid models and Neural Differential Equations (NDE) are getting increasingly important for the modeling of physical systems, however they often encounter stability and accuracy issues during long-term integration. Training on unrolled trajectories is known to limit these divergences but quickly be…

• SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion

  Sedjro Salomon Hotegni, Sebastian Peitz · 5 février 2026

  Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we introduce SPREAD, a generative framework based on Denoising Dif…

• Turning mechanistic models into forecasters by using machine learning

  Amit K. Chakraborty, Hao Wang, Pouria Ramazi · 5 février 2026

  The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from time-series data using a library of functions constructed from the mea…