相关论文: Physics-based machine learning for modeling stocha…

Model predictive control (MPC) schemes have a proven track record for delivering aggressive and robust performance in many challenging control tasks, coping with nonlinear system dynamics, constraints, and observational noise. Despite their…

We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…

We demonstrate that embedding physics-driven constraints into machine learning process can dramatically improve accuracy and generalizability of the resulting model. Physics-informed learning is illustrated on the example of analysis of…

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Combining physics with machine learning models has advanced the performance of machine learning models in many different applications. In this paper, we evaluate adding a weak physics constraint, i.e., a physics-based empirical…

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

Synaptic transmission between neurons is governed by a cascade of stochastic reaction-diffusion events that lead to calcium-induced vesicle release of neurotransmitter. Since experimental measurements of such systems are challenging due…

Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite…

In this work we consider the semi-batch process of precipitation of calcium carbonate solids from a solution containing calcium ions by adjusting the pH of the solution. The change in pH is induced either by the addition of alkaline…

Intracellular calcium is regulated in part by the release of Ca$^{2+}$ ions from the endoplasmic reticulum via inositol-4,5-triphosphate receptor (IP$_3$R) channels (among other possibilities such as RyR and L-type calcium channels). The…

Can a micron sized sack of interacting molecules autonomously learn an internal model of a complex and fluctuating environment? We draw insights from control theory, machine learning theory, chemical reaction network theory, and statistical…

In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction…

In contact-rich tasks, the hybrid, multi-modal nature of contact dynamics poses great challenges in model representation, planning, and control. Recent efforts have attempted to address these challenges via data-driven methods, learning…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…

Nonlocal models have recently had a major impact in nonlinear continuum mechanics and are used to describe physical systems/processes which cannot be accurately described by classical, calculus based "local" approaches. In part, this is due…