Related papers: Hybrid Neural Network Augmented Physics-based Mode…

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such…

A hybrid machine learning and process-based-modeling (PBM) approach is proposed and evaluated at a handful of AmeriFlux sites to simulate the top-layer soil moisture state. The Hybrid-PBM (HPBM) employed here uses the Noah land-surface…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…

Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing…

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

Physics-guided neural networks (PGNN) is an effective tool that combines the benefits of data-driven modeling with the interpretability and generalization of underlying physical information. However, for a classical PGNN, the penalization…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Agent Based Modelling (ABM) is a computational framework for simulating the behaviours and interactions of autonomous agents. As Agent Based Models are usually representative of complex systems, obtaining a likelihood function of the model…

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring…

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…

State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…

In this paper, we consider Hybrid Mixed Networks (HMN) which are Hybrid Bayesian Networks that allow discrete deterministic information to be modeled explicitly in the form of constraints. We present two approximate inference algorithms for…

Agent-based modelling (ABMing) is a powerful and intuitive approach to modelling complex systems; however, the intractability of ABMs' likelihood functions and the non-differentiability of the mathematical operations comprising these models…

A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…

Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions…

Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…