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The machine learning (ML) techniques to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar models is employed. The effectiveness of this approach is demonstrated by applying it to the two and three Higgs…
Machine learning (ML) is the field of training machines to achieve high level of cognition and perform human-like analysis. Since ML is a data-driven approach, it seemingly fits into our daily lives and operations as well as complex and…
As microstructure property models improve, additional information from crystallographic degrees of freedom and grain boundary networks (GBNs) can be included in microstructure design problems. However, the high dimensional nature of…
We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…
In recent years, the use of Machine Learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising…
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…
This paper presents a comprehensive study on stock price prediction, leveragingadvanced machine learning (ML) and deep learning (DL) techniques to improve financial forecasting accuracy. The research evaluates the performance of various…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…
Mean field games (MFGs) provide a mathematically tractable framework for modelling large-scale multi-agent systems by leveraging mean field theory to simplify interactions among agents. It enables applying inverse reinforcement learning…
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…
In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…
Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that…
The investigation of finite temperature properties using Monte-Carlo (MC) methods requires a large number of evaluations of the system's Hamiltonian to sample the phase space needed to obtain physical observables as function of temperature.…
The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation…
Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…
We review recent advances in machine-learning (ML) force-field methods for large-scale Landau-Lifshitz-Gilbert (LLG) simulations of metallic spin systems. We generalize the Behler-Parrinello (BP) ML architecture -- originally developed for…