Related papers: On Higher Order Drift and Diffusion Estimates for …
In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
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…
Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…
The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
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…
Microgrids (MGs) play a crucial role in utilizing distributed energy resources (DERs) like solar and wind power, enhancing the sustainability and flexibility of modern power systems. However, the inherent variability in MG topology, power…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Road user trajectory prediction in dynamic environments is a challenging but crucial task for various applications, such as autonomous driving. One of the main challenges in this domain is the multimodal nature of future trajectories…
We propose a conditional stochastic interpolation (CSI) method for learning conditional distributions. CSI is based on estimating probability flow equations or stochastic differential equations that transport a reference distribution to the…
This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…
This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…
The problem of drift estimation for the solution $X$ of a stochastic differential equation with L\'evy-type jumps is considered under discrete high-frequency observations with a growing observation window. An efficient and asymptotically…
In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on…