Related papers: Hybridizing Physical and Data-driven Prediction Me…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design…

We propose a Bayesian nonparametric model for mixed-type bounded data, where some variables are compositional and others are interval-bounded. Compositional variables are non-negative and sum to a given constant, such as the proportion of…

A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

In this article, we propose a covariance based method for combining partial data sets in the genotype to phenotype spectrum. In particular, an expectation-maximization algorithm that can be used to combine partially overlapping…

We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…

In this study, we leverage a mixture model learning approach to identify defects in laser-based Additive Manufacturing (AM) processes. By incorporating physics based principles, we also ensure that the model is sensitive to meaningful…

We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic applications. Both dense fluid and dilute gas formulations are considered. The choice of coupling method and its relation to the fluid physics is discussed. The…

Accurate demand forecasting is vital for ensuring reliable access to contraceptive products, supporting key processes like procurement, inventory, and distribution. However, forecasting contraceptive demand in developing countries presents…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using…

Spatially misaligned data can be fused by using a Bayesian melding model that assumes that underlying all observations there is a spatially continuous Gaussian random field process. This model can be used, for example, to predict air…

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

We introduce a framework to dynamically combine heterogeneous models called \texttt{DYCHEM}, which forecasts a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as…

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic…

We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…

A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…