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How is it that humans can solve complex planning tasks so efficiently despite limited cognitive resources? One reason is its ability to know how to use its limited computational resources to make clever choices. We postulate that people…

Although the Poincare' and the geometrization conjectures were recently proved by Perelman, the proof relies heavily on properties of the Ricci flow previously investigated in great detail by Hamilton. Physical realization of such a flow…

Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…

Deep reinforcement learning has achieved many impressive results in recent years. However, tasks with sparse rewards or long horizons continue to pose significant challenges. To tackle these important problems, we propose a general…

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

Although learning from data is effective and has achieved significant milestones, it has many challenges and limitations. Learning from data starts from observations and then proceeds to broader generalizations. This framework is…

We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine…

Machine learning (ML) methods, which fit to data the parameters of a given parameterized model class, have garnered significant interest as potential methods for learning surrogate models for complex engineering systems for which…

We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the…

Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy.…

Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest in recent times from dispersed multiphase flow community. The robustness of neural models for this complex multi-body…

This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…

"AI for science" is widely recognized as a future trend in the development of scientific research. Currently, although machine learning algorithms have played a crucial role in scientific research with numerous successful cases, relatively…

The Poincar\'e (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincar\'e group. The physical laws are formulated in terms of points,…

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily…

In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In…

Data collection in economically constrained countries often necessitates using approximate and biased measurements due to the low-cost of the sensors used. This leads to potentially invalid predictions and poor policies or decision making.…

Applications of neural networks to data analyses in natural sciences are complicated by the fact that many inputs are subject to systematic uncertainties. To control the dependence of the neural network function to variations of the input…