Related papers: Parameter estimation of high-dimensional linear di…
In an Markov decision process (MDP), unobservable confounders may exist and have impacts on the data generating process, so that the classic off-policy evaluation (OPE) estimators may fail to identify the true value function of the target…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
There has been a long history of using ordinary differential equations (ODEs) to understand the dynamics of discrete-time algorithms (DTAs). Surprisingly, there are still two fundamental and unanswered questions: (i) it is unclear how to…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…
First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…