Related papers: Physics-informed Information Field Theory for Mode…
A new class of functions, called the `Information sensitivity functions' (ISFs), which quantify the information gain about the parameters through the measurements/observables of a dynamical system are presented. These functions can be…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
This paper introduces a physics-informed machine learning approach for pathloss prediction. This is achieved by including in the training phase simultaneously (i) physical dependencies between spatial loss field and (ii) measured pathloss…
Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on…
We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…
Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space…
We consider the problem of a robot learning the mechanical properties of objects through physical interaction with the object, and introduce a practical, data-efficient approach for identifying the motion models of these objects. The…
Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…
Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…
Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…
Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…