Related papers: Data-driven computational mechanics
Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the…
Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
In this paper, we propose a novel data-driven predictive control approach for systems subject to time-domain constraints. The approach combines the strengths of H-infinity control for rejecting disturbances and MPC for handling constraints.…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
A main challenge of data-driven sciences is how to make maximal use of the progressively expanding databases of experimental datasets in order to keep research cumulative. We introduce the idea of a modeling-based dataset retrieval engine…
Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that…
Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…
A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system…
We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Managing supply and demand in the electricity grid is becoming more challenging due to the increasing penetration of variable renewable energy sources. As significant end-use consumers, and through better grid integration, buildings are…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to…
The design of data-driven formulations for machine learning and decision-making with good out-of-sample performance is a key challenge. The observation that good in-sample performance does not guarantee good out-of-sample performance is…