Related papers: An attention-based neural ordinary differential eq…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…

Ionic models, the set of ordinary differential equations (ODEs) describing the time evolution of the state of excitable cells, are the cornerstone of modeling in neuro- and cardiac electrophysiology. Modern ionic models can have tens of…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

This paper introduces Stress-Aware Learning, a resilient neural training paradigm in which deep neural networks dynamically adjust their optimization behavior - whether under stable training regimes or in settings with uncertain dynamics -…

Deep selective State-Space Models (SSMs), whose state-space parameters are modulated online by a selection signal, offer significant expressive power but pose challenges for stability analysis, especially under discontinuous gating. We…

We propose a scalable, approximate inference hypernetwork framework for a general model of history-dependent processes. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of…

In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…

This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…

Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We…

Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation…

We investigate a conductance-based neuron model to explore how voltage-gated ion channel isoforms influence action-potential generation. The model combines a six-state Markov representation of NaV channels with a first-order KV3.1 model,…

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…

We develop a new neural network architecture that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the…

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…