Related papers: Parameter Estimation via Fokker-Planck Type Residu…
There is recent interest in finding a potential formulation for Stochastic Partial Differential Equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of…
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that…
We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded…
The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
In this paper, we study policy evaluation in continuous-time reinforcement learning (RL), where the state follows an unknown stochastic differential equation (SDE), but only discrete-time data are available. We first highlight that the…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
The existence of random dynamical systems for McKean--Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a change of stability measured with a small parameter $\varepsilon$, we rely on the natural…
We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main…
We introduce a parameter estimation method that utilizes microscopic data, specifically averages and correlations of selected microscopic observables, to determine the parameters of a stochastic differential equation governing…
We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random…
A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the…