Related papers: Neural Langevin Dynamics: towards interpretable Ne…

We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation (GLE) with a homogeneous kernel. The constructed model naturally…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD),…

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…

We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of…

By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models,…

This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the…

Deep neural networks have revolutionized machine learning, yet their training dynamics remain theoretically unclear-we develop a continuous-time, matrix-valued stochastic differential equation (SDE) framework that rigorously connects the…

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations. We use Diffusion Maps…

We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential…

Recent approaches for modelling dynamics of physical systems with neural networks enforce Lagrangian or Hamiltonian structure to improve prediction and generalization. However, when coordinates are embedded in high-dimensional data such as…