Related papers: Non-Negative Universal Differential Equations With…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…
Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. Equational unification is of special relevance to automated deduction, theorem…
Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their…
A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of…
It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…
Unlearnable examples (UEs) aim to compromise model training by injecting imperceptible perturbations to clean samples. However, existing UE schemes exhibit limited robustness against advanced defenses due to their heuristic design or…
To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…
Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…
Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural…
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an $m$-dimensional Brownian motion and a $d$-dimensional canonical process with uniform Lipschitzian coefficients. Such…
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include…
It is demonstrated that very general nonlinear dynamical systems covering all cases arising in practice can be brought down to rate equations of chemical kinetics
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…