16,977 research outputs found
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)
We show how a complete mathematical description of a complicated physical
phenomenon can be learned from observational data via a hybrid approach
combining three simple and general ingredients: physical assumptions of
smoothness, locality, and symmetry, a weak formulation of differential
equations, and sparse regression. To illustrate this, we extract a system of
governing equations describing flows of incompressible Newtonian fluids -- the
Navier-Stokes equation, the continuity equation, and the boundary conditions --
from numerical data describing a highly turbulent channel flow in three
dimensions. These relations have the familiar form of partial differential
equations, which are easily interpretable and readily provide information about
the relative importance of different physical effects as well as insight into
the quality of the data, serving as a useful diagnostic tool. The approach
described here is remarkably robust, yielding accurate results for very high
noise levels, and should thus be well-suited to experimental data
Learning stable and predictive structures in kinetic systems: Benefits of a causal approach
Learning kinetic systems from data is one of the core challenges in many
fields. Identifying stable models is essential for the generalization
capabilities of data-driven inference. We introduce a computationally efficient
framework, called CausalKinetiX, that identifies structure from discrete time,
noisy observations, generated from heterogeneous experiments. The algorithm
assumes the existence of an underlying, invariant kinetic model, a key
criterion for reproducible research. Results on both simulated and real-world
examples suggest that learning the structure of kinetic systems benefits from a
causal perspective. The identified variables and models allow for a concise
description of the dynamics across multiple experimental settings and can be
used for prediction in unseen experiments. We observe significant improvements
compared to well established approaches focusing solely on predictive
performance, especially for out-of-sample generalization
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