Model Reduction and Neural Networks

Derniers papiers

• A Hyperbolic Neural Closure for M1 Radiation Transfer

  Bongseok Kim, Jiahao Zhang, Johannes Krotz, Dinshaw Balsara, Ryan McClarren, Guang Lin · 14 juillet 2026

  In radiation transfer simulations, an M1 method achieves substantial computational savings by replacing the full angular transport equation with a low-order moment system. Because this reduced system is not closed, a closure model is required to represent the unknown higher-order moments using lower…

• Robustly Invertible Nonlinear Dynamics and the BiLipREN: From Inversion-Based Control to Generative Trajectory Modelling

  Yurui Zhang, Ruigang Wang, Ian R. Manchester · 14 juillet 2026

  This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design. We define robust invertibility as the existence of a causal inverse system such that both the f…

• Diversify Diffusion with Temperature Sampling and Variance-Corrective Time Shifting

  Peizhuo Li, Emre Aksan, Alexandru-Eugen Ichim, Thabo Beeler, Olga Sorkine-Hornung · 14 juillet 2026

  Diffusion models faithfully reproduce their training distribution, but also inherit its imbalances and leave rare or under-represented modes hard to reach. A natural inference-time remedy is to sample from the high-temperature target $p^{(\gamma)}_0(x) \propto p_0(x)^{\gamma}$ for $0 < \gamma < 1$, …

• SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

  Divyavardhan Singh, Dimple Sonone, Hammad Mohammad, Kishor Upla · 14 juillet 2026

  Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-cau…

• Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks

  Aruzhan Tleubek, Salah A Faroughi · 14 juillet 2026

  Discovering the memory or nonlocal kernel governing an integro-differential equation (IDE) from sparse and noisy observations is an ill-posed inverse problem. Existing identification methods often rely on problem-specific analytical derivations, specialized observation requirements, or restrictive a…

• A multi-scale feature enhanced graph neural network for fluid dynamics prediction in complex geometries

  Li Xiao, Tianyu Li, Yiye Zou, Mingjie Zhang, Xiaogangd Deng · 14 juillet 2026

  Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs. Deep neural networks have shown promise in improving simulation efficiency, especially grap…

• Implicit Neural Networks as Static Controllers: Certificates and Performance Separation

  Giuseppe C. Calafiore, Laurent El Ghaoui · 14 juillet 2026

  Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller…

• Heuristic Learning for Active Flow Control Using Coding Agents

  Paul Garnier, Jonathan Viquerat, Elie Hachem · 14 juillet 2026

  Active flow control involves nonlinear dynamics, partial observations, and computationally expensive simulations, making controller design particularly challenging. Deep reinforcement learning (DRL) has emerged as a powerful framework for such problems, but its success typically relies on large numb…

• The Differential Neural Tangent Kernel and Its Positivity

  Bangti Jin, Longjun Wu · 14 juillet 2026

  The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime. Recently, the theoretical framework has been extended to physics-informed neural networks (PINNs) for solving linear PDEs, one highly popular class of neural …

• Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

  Zhangyi Lian, Xinda Dong, Wenxuan Huo, Weifeng Huang, Gang Zhu, Qiang He · 14 juillet 2026

  Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical informat…

• Backpropagation as a Nilpotent Linear System

  Ahmed Boughammoura · 14 juillet 2026

  Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs. We present a global operator theory of the \emph{F-adjoint} framework, which reformulates the layerwise backward recursion of an $L$-de…

• SKooP: Symmetric Koopman Predictions for Faster and More Generalizable Legged Robot Locomotion with Reinforcement Learning

  Evelyn D'Elia, Weishu Zhan, Giulio Turrisi, Giulio Romualdi, Giuseppe L'Erario, Raffaello Camoriano, Wei Pan, Daniele Pucci · 14 juillet 2026

  Reinforcement learning (RL) algorithms classically suffer from poor sample efficiency. In robotics, a recent line of work has emerged addressing this problem by encoding physics priors in the learning process. However, most of these approaches are validated on well-defined, low-dimensional benchmark…

• Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensors

  Tudor Bartha, Radu Chiorean, Adrian Groza · 14 juillet 2026

  This paper presents a machine learning framework for data-driven inverse design of V-beam thermal sensors. The goal is to determine the optimal sensor geometry: beam inclination angle, beam length and beam width that achieves a target displacement under a given temperature. The design should also pr…

• Discovering Latent Response Laws in Forced Physical Systems

  Yi Zhu, Su Chen, Xiaojun Li, Xiuli Du · 14 juillet 2026

  Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we intro…

• Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

  Pengfei Cai, Utkarsh Utkarsh, Alan Edelman, Christopher Vincent Rackauckas, Rafael Gomez-Bombarelli · 14 juillet 2026

  Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has begun to frame PDE …

• Velocity Scheduled Flow Matching

  Vitalii Bondar · 14 juillet 2026

  Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout …

• IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry

  Ying Yan, Liwei Hu, Xiaoming Zhang · 14 juillet 2026

  Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of …

• Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry

  Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu · 13 juillet 2026

  This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains. We propose a physics-informed DeepONet framework that predicts displacement fields from both boundary conditions and fracture geometry, using a dedicate…

• Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models

  Eli Laird, Corey Clark · 10 juillet 2026

  World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that mus…

• LLT: Local Linear Transformer for PDE Operator Learning

  Oded Ovadia, Eli Turkel · 10 juillet 2026

  Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two majo…

• Neural non-canonical Hamiltonian dynamics for long-time simulations

  Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML) · 10 juillet 2026

  This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet, respectively with a potential-based architecture and with degen…

• An optimal control approach for neural network architecture adaptation with a posteriori error estimation

  C G Krishnanunni, Thomas Scott, Tan Bui-Thanh · 9 juillet 2026

  This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a continuous-time optimal control problem, we derive rigorous error estimates that quantify how approximation error distribut…

• Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design

  Rebecca M. Crossley, Yuan Yin, Sarah L. Waters, Ruth E. Baker · 9 juillet 2026

  Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding mechanistic differential equations into neural network…

• Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates

  Jianing Liu, Dong H. Zhang · 9 juillet 2026

  Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects…

• Quantum simulation of real-world nonlinear dynamics via Koopman method

  Baoyang Zhang, Dong An, Zhaoyuan Meng, Yefei Yu, Xiaoxiao Xiao, Zhen Lu, Yue Yang · 9 juillet 2026

  Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear …