Related papers: \texttt{calypso}: a Parameter-Conditioned Stochast…

Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random…

We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…

Healthcare data often come from multiple sites in which the correlations between confounding variables can vary widely. If deep learning models exploit these unstable correlations, they might fail catastrophically in unseen sites. Although…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

Multivariate mixed-type outcomes are difficult to model jointly, and additional complexity arises when both marginal effects and dependence structures vary with a covariate such as age or time. Existing approaches often impose restrictive…

Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Robust and efficient mathematical…

Many control problems require repeated tuning and adaptation of controllers across distinct closed-loop tasks, where data efficiency and adaptability are critical. We propose a hierarchical Bayesian optimization (BO) framework that is…

Mechanistic, multicellular, agent-based models are commonly used to investigate tissue, organ, and organism-scale biology at single-cell resolution. The Cellular-Potts Model (CPM) is a powerful and popular framework for developing and…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic…

Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in…

The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future,…

Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal…

Alternative formulations for the optimization of chemical process flowsheets are presented that leverage surrogate models and implicit functions to replace and remove, respectively, the algebraic equations that describe a…

Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as…

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

Due to the need for robust uncertainty quantification, Bayesian neural learning has gained attention in the era of deep learning and big data. Markov Chain Monte-Carlo (MCMC) methods typically implement Bayesian inference which faces…

A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO)…

Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…