Related papers: Data-driven Feynman-Kac Discovery with Application…
The classical Feynman-Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing stochastic representations for classical solutions of linear Kolmogorov PDEs. This opens the door for the…
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor $F_*$, namely, between a stochastic differential equation and a dynamical system on a statistical manifold, and…
A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is…
We propose a probabilistic model discovery method for identifying ordinary differential equations (ODEs) governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy)…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…
We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations…
We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification…
A backward stochastic differential equation (BSDE) is an SDE of the form $-dY_t = f(t,Y_t,Z_t)dt - Z_t^*dW_t;\ Y_T = \xi$. The subject of BSDEs has seen extensive attention since their introduction in the linear case by Bismut (1973) and in…
We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…
We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differential equations (SDEs). In the deterministic setting, three…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming…