Related papers: Fast derivatives of likelihood functionals for ODE…
Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
We propose a homotopy continuation method called FLUX for approximating complicated probability density functions. It is based on progressive processing for smoothly morphing a given density into the desired one. Distributed ordinary…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show…
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…
Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive…
In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…
In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…