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We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f$ for an FPT problem $\Pi$ on a graph $G$ with parameter $k$…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
This work presents an illustrative application of the second-order adjoint sensitivity analysis procedure (SO-ASAP) to a paradigm neutron diffusion problem, which is sufficiently simple to admit an exact solution, thereby making transparent…
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Designing clinical trials requires evaluating multiple operating characteristics (OCs), such as the likelihood of an early stopping decision, the probability of detecting a treatment effect, and the Type I error rate. In most cases, these…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
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 article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the behavior of an operator, such that the resulting neural network…
The use of simulation-based sensitivity analyses is fundamental to evaluate and compare candidate designs for future clinical trials. In this context, sensitivity analyses are especially useful to assess the dependence of important design…
Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse…