Model Reduction and Neural Networks

Derniers papiers

• Neuro-Symbolic ODE Discovery with Latent Grammar Flow

  Karin Yu, Eleni Chatzi, Georgios Kissas · 20 avril 2026

  Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a neuro-symbolic generative framework for discovering ordinary dif…

• Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)

  Tomasz S{\l}u\.zalec, Marcin {\L}o\'s, Askold Vilkha, Maciej Paszy\'nski · 20 avril 2026

  We explore the possibility of solving Partial Differential Equations (PDEs) using discrete weak formulations. We propose a programming environment for defining a discrete computational domain, introducing discrete functions defined over a set of points, constructing discrete inner products, and intr…

• Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks

  Kang An, Chenhao Si, Shiqian Ma, Ming Yan · 20 avril 2026

  Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss landscapes. We propose a lightweight curvature-aware optimization fr…

• A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws

  Jiamin Jiang, Shanglin Lv, Jingrun Chen · 20 avril 2026

  Hyperbolic conservation laws govern a wide range of transport-driven dynamics featuring shocks, contact discontinuities, and complex wave interactions, posing distinct challenges for deep-learning-based surrogate modeling. While classical numerical methods provide robust and physically admissible so…

• PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs

  Shimon Pisnoy, Hemanth Chandravamsi, Ziv Chen, Aaron Goldgewert, Gal Shaviner, Boris Shragner, Steven H. Frankel · 20 avril 2026

  We present PINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow. The framework enables systematic evaluation of PI…

• Structural interpretability in SVMs with truncated orthogonal polynomial kernels

  V\'ictor Soto-Larrosa, Nuria Torrado, Edmundo J. Huertas · 17 avril 2026

  We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product orthonormal basis, the fitted decision function can be expa…

• Auxiliary Finite-Difference Residual-Gradient Regularization for PINNs

  Stavros Kassinos · 17 avril 2026

  Physics-informed neural networks (PINNs) are often selected by a single scalar loss even when the quantity of interest is more specific. We study a hybrid design in which the governing PDE residual remains automatic-differentiation (AD) based, while finite differences (FD) appear only in a weak auxi…

• SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems

  Murat Furkan Mansur, Tufan Kumbasar · 17 avril 2026

  Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Info…

• Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design

  Sudeepta Mondal, Soumalya Sarkar · 17 avril 2026

  Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However, these simulations are often high-fidelity in nature, and can …

• Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs

  Kentaro Hoshisashi, Carolyn E Phelan, Paolo Barucca · 16 avril 2026

  Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as fundamental as the governing equations. In this paper, we present De…

• AeTHERON: Autoregressive Topology-aware Heterogeneous Graph Operator Network for Fluid-Structure Interaction

  Sushrut Kumar · 16 avril 2026

  Surrogate modeling of body-driven fluid flows where immersed moving boundaries couple structural dynamics to chaotic, unsteady fluid phenomena remains a fundamental challenge for both computational physics and machine learning. We present AeTHERON, a heterogeneous graph neural operator whose archite…

• Randomized Neural Networks for Integro-Differential Equations with Application to Neutron Transport

  Haoning Dang, Fei Wang, Yifan Chen, Zhouyu Liu, Dong Liu, Hongchun Wu · 16 avril 2026

  Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such nonlocality often introduces dense coupling blocks in deterministic…

• Physics-informed reservoir characterization from bulk and extreme pressure events with a differentiable simulator

  Harun Ur Rashid, Mingxin Li, Aleksandra Pachalieva, Georg Stadler, Daniel O'Malley · 16 avril 2026

  Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and CO$_2$, H$_2$, and wastewater injection operations. This challenge becomes especially acute in extreme pressure events, which ar…

• Diffusion Sequence Models for Generative In-Context Meta-Learning of Robot Dynamics

  Angelo Moroncelli, Matteo Rufolo, Gunes Cagin Aydin, Asad Ali Shahid, Loris Roveda · 16 avril 2026

  Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem and compare deterministic and generative sequence models fo…

• Fast and principled equation discovery from chaos to climate

  Yuzheng Zhang, Weizhen Li, Rui Carvalho · 15 avril 2026

  Our ability to predict, control, and ultimately understand complex systems rests on discovering the equations that govern their dynamics. Identifying these equations directly from noisy, limited observations has therefore become a central challenge in data-driven science, yet existing library-based …

• Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems

  Ananda Chakrabarti, Haitham H. Saleh, Indranil Nayak, Balasubramaniam Shanker, Fernando L. Teixeira, Debdipta Goswami · 15 avril 2026

  We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators an…

• Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs

  Etienne Boursier, Loucas Pillaud-Vivien, Nicolas Flammarion · 15 avril 2026

  The training of neural networks by gradient descent methods is a cornerstone of the deep learning revolution. Yet, despite some recent progress, a complete theory explaining its success is still missing. This article presents, for orthogonal input vectors, a precise description of the gradient flow …

• Inter-Layer Hessian Analysis of Neural Networks with DAG Architectures

  Maxim Bolshim (ITMO University, Saint Petersburg, Russia), Alexander Kugaevskikh (ITMO University, Saint Petersburg, Russia) · 14 avril 2026

  Modern automatic differentiation frameworks (JAX, PyTorch) return the Hessian of the loss function as a monolithic tensor, without exposing the internal structure of inter-layer interactions. This paper presents an analytical formalism that explicitly decomposes the full Hessian into blocks indexed …

• Agentic Exploration of PDE Spaces using Latent Foundation Models for Parameterized Simulations

  Abhijeet Vishwasrao, Francisco Giral, Mahmoud Golestanian, Federica Tonti, Andrea Arroyo Ramo, Adrian Lozano-Duran, Steven L. Brunton, Sergio Hoyas, Soledad Le Clainche, Hector Gomez, Ricardo Vinuesa · 14 avril 2026

  Flow physics and more broadly physical phenomena governed by partial differential equations (PDEs), are inherently continuous, high-dimensional and often chaotic in nature. Traditionally, researchers have explored these rich spatiotemporal PDE solution spaces using laboratory experiments and/or comp…

• Knowledge Integration in Differentiable Models: A Comparative Study of Data-Driven, Soft-Constrained, and Hard-Constrained Paradigms for Identification and Control of the Single Machine Infinite Bus System

  Shinhoo Kang, Sangwook Kim, Sehyun Yun · 14 avril 2026

  Integrating domain knowledge into neural networks is a central challenge in scientific machine learning. Three paradigms have emerged -- data-driven (Neural Ordinary Differential Equations, NODEs), soft-constrained (Physics-Informed Neural Networks, PINNs), and hard-constrained (Differentiable Progr…

• Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks

  Yuto Omae, Kazuki Sakai, Yohei Kakimoto, Makoto Sasaki, Yusuke Sakai, Hirotaka Takahashi · 14 avril 2026

  Neural networks (NNs) are central to modern machine learning and achieve state-of-the-art results in many applications. However, the relationship between loss geometry and generalization is still not well understood. The local geometry of the loss function near a critical point is well-approximated …

• Physics and causally constrained discrete-time neural models of turbulent dynamical systems

  Fabrizio Falasca, Laure Zanna · 14 avril 2026

  We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of temporally discrete trajectories. We then impose causal const…

• SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

  Samrendra Roy, Souvik Chakraborty, Rizwan-uddin, Syed Bahauddin Alam · 14 avril 2026

  Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking C…

• Design Principles for Sequence Models via Coefficient Dynamics

  Jerome Sieber, Antonio Orvieto, Melanie N. Zeilinger, Carmen Amo Alonso · 14 avril 2026

  Deep sequence models, ranging from Transformers and State Space Models (SSMs) to more recent approaches such as gated linear RNNs, fundamentally compute outputs as linear combinations of past value vectors. To draw insights and systematically compare such architectures, we develop a unified framewor…

• Learning to Test: Physics-Informed Representation for Dynamical Instability Detection

  Minxing Zheng, Zewei Deng, Liyan Xie, Shixiang Zhu · 14 avril 2026

  Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate under stochastically varying environmental inputs, so stabili…