Related papers: Minimization of Dynamical Systems over Monoids
Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…
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…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
Machine learning force fields show great promise in enabling more accurate molecular dynamics simulations compared to manually derived ones. Much of the progress in recent years was driven by exploiting prior knowledge about physical…
Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…
Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several…
Gradient-based Bi-Level Optimization (BLO) methods have been widely applied to handle modern learning tasks. However, most existing strategies are theoretically designed based on restrictive assumptions (e.g., convexity of the lower-level…
Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization…
Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively…
By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new…
Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special…
Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic…
Bayesian optimization (BO) struggles in high dimensions, where Gaussian-process surrogates demand heavy retraining and brittle assumptions, slowing progress on real engineering and design problems. We introduce GIT-BO, a Gradient-Informed…
The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
Channel estimation and beamforming play critical roles in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. However, these two modules have been treated as two stand-alone components, which makes it…