Related papers: SING: SDE Inference via Natural Gradients
Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…
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…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…
Stochastic models with global parameters and latent variables are common, and for which variational inference (VI) is popular. However, existing methods are often either slow or inaccurate in high dimensions. We suggest a fast and accurate…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…
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…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in mechanical and infrastructural systems. Since degradation is rarely directly observable and measurable, it must be inferred…
Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing…
Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…
Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering,…