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Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…
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While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
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Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…
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Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Python has become the de facto language for scientific computing. Programming in Python is highly productive, mainly due to its rich science-oriented software ecosystem built around the NumPy module. As a result, the demand for Python…
Earth system models are developed with a tight coupling to target hardware, often containing specialized code predicated on processor characteristics. This coupling stems from using imperative languages that hard-code computation schedules…
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The introduction of Physics-informed Neural Networks (PINNs) has led to an increased interest in deep neural networks as universal approximators of PDEs in the solid mechanics community. Recently, the Deep Energy Method (DEM) has been…
Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…