Related papers: Neural Langevin Dynamics: towards interpretable Ne…

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it…

Illumination variation has been a long-term challenge in real-world facial expression recognition(FER). Under uncontrolled or non-visible light conditions, Near-infrared (NIR) can provide a simple and alternative solution to obtain…

Handling static images that lack inherent temporal dynamics remains a fundamental challenge for spiking neural networks (SNNs). In directly trained SNNs, static inputs are typically repeated across time steps, causing the temporal dimension…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Stochastic Gradient Descent Langevin Dynamics (SGLD) algorithms, which add noise to the classic gradient descent, are known to improve the training of neural networks in some cases where the neural network is very deep. In this paper we…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase.…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic…

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Trajectory generation and trajectory prediction are two critical tasks in autonomous driving, which generate various trajectories for testing during development and predict the trajectories of surrounding vehicles during operation,…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…