Related papers: Neural Closure Models for Dynamical Systems

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…

This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations…

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…

If sufficient training data are available, neural networks are attractive for representing missing physics in simulations, such as sub-grid scales in the coarse-mesh particle-turbulence system we consider. Physical constraints are known to…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…

Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Neural operators have demonstrated promise in modeling and controlling systems governed by Partial Differential Equations (PDEs). Beyond PDEs, Stochastic Partial Differential Equations (SPDEs) play a critical role in modeling systems…

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct…

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of…

Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in…

Deep learning has advanced from fully connected architectures to structured models organized into components, e.g., the transformer composed of positional elements, modular architectures divided into slots, and graph neural nets made up of…