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Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG),…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and demands…
Contemporary intelligent systems incorporate software components, including machine learning components. As they grow in complexity and data volume such machine learning systems face unique quality challenges like scalability and…
Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML…
This paper introduced key aspects of applying Machine Learning (ML) models, improved trading strategies, and the Quasi-Reversibility Method (QRM) to optimize stock option forecasting and trading results. It presented the findings of the…
Machine learning force fields (MLFFs) are a promising approach to balance the accuracy of quantum mechanics with the efficiency of classical potentials, yet selecting an optimal model amid increasingly diverse architectures that delivers…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…
Here, we examine the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field games (MFG). In the first part of this paper, we present the Wardrop and the first-order MFG models on…
Machine learning (ML) is a revolutionary technology with demonstrable applications across multiple disciplines. Within the Earth science community, ML has been most visible for weather forecasting, producing forecasts that rival modern…
Maximum likelihood (ML) and adversarial learning are two popular approaches for training generative models, and from many perspectives these techniques are complementary. ML learning encourages the capture of all data modes, and it is…
Machine learning (ML) models are increasingly being used in metrology applications. However, for ML models to be credible in a metrology context they should be accompanied by principled uncertainty quantification. This paper addresses the…
Interatomic potential models based on machine learning (ML) are rapidly developing as tools for materials simulations. However, because of their flexibility, they require large fitting databases that are normally created with substantial…
Additive Manufacturing (AM) is a transformative manufacturing technology enabling direct fabrication of complex parts layer-be-layer from 3D modeling data. Among AM applications, the fabrication of Functionally Graded Materials (FGMs) has…
Machine learning (ML)-based solutions are rapidly changing the landscape of many fields, including structural engineering. Despite their promising performance, these approaches are usually only demonstrated as proof-of-concept in structural…
This paper describes a reference architecture for self-maintaining systems that can learn continually, as data arrives. In environments where data evolves, we need architectures that manage Machine Learning (ML) models in production, adapt…
In this paper, we argue that the prevailing approach to training and evaluating machine learning models often fails to consider their real-world application within organizational or societal contexts, where they are intended to create…
This paper introduces the Minimum Price Markov Game (MPMG), a theoretical model that reasonably approximates real-world first-price markets following the minimum price rule, such as public auctions. The goal is to provide researchers and…