There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A central challenge is reconciling data that is at odds with simplified models without requiring "big data". 
In this work we develop a new methodology, universal differential equations (UDEs), which augments scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating the training of physics-informed neural networks and large-eddy simulations, can all be transformed into UDE training problems that are efficiently solved by a single software methodology.

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Universal Differential Equations for Scientific Machine Learning

Thermo-Fluid Dynamics of Two-Phase Flow

Argonne National Laboratory 滞在記

Data-driven modeling for boiling heat transfer: Using deep neural networks and high-fidelity simulation results

SAM Theory Manual

Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model

Inverse uncertainty quantification of trace physical model parameters using BFBT benchmark data

A roe-type numerical solver for the two-phase two-fluid six-equation model with realistic equation of state

/pdf/multi-physics-simulations-of-heat-pipe-micro-reactor-mqj3il458r.pdf

Guojun Hu

Papers

SAM Theory Manual

Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model

Inverse uncertainty quantification of trace physical model parameters using BFBT benchmark data

A roe-type numerical solver for the two-phase two-fluid six-equation model with realistic equation of state

Multi-Physics Simulations of Heat Pipe Micro Reactor