Gradient-based Inference for Networks with Output Constraints

Lee, Jay Yoon; Mehta, Sanket Vaibhav; Wick, Michael J.; Tristan, Jean-Baptiste; Carbonell, Jaime G.

doi:10.48550/arxiv.1707.08608

Cited by 1 publication

(3 citation statements)

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“…The second, more general method to build constraint-aware neural networks is based on the idea of penalizing deviations from the constraint (11) during the training procedure (as mentioned in [27,22]) . To this end, we introduce the constraint loss function…”

Section: Constraint-adapted Loss Methods (Cal)mentioning

confidence: 99%

“…which will be the constraint that a surrogate model for (21) should satisfy. As in (12) the constraint target function Φ cubic : × × , corresponding to (22), is given by…”

Section: Cubic Flux Model: Undercompressive Wavementioning

confidence: 99%

“…In [22] unconstrained neural networks are combined with an optimization algorithm during test time to resolve constraints in the context of parsing problems. A probabilistic approach to a ne-linear constraints was proposed in [34].…”

Section: Introductionmentioning

confidence: 99%

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Constraint-aware neural networks for Riemann problems

Magiera

Ray

Hesthaven

et al. 2020

Journal of Computational Physics

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Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satis ed to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints. We propose two di erent strategies to generate constraint-aware neural networks. We test their performance in the context of front-capturing schemes for strongly nonlinear wave motion in compressible uid ow. Precisely, in this context so-called Riemann problems have to be solved as surrogates. Their solution describes the local dynamics of the captured wave front in numerical simulations. Three model problems are considered: a cubic ux model problem, an isothermal two-phase ow model, and the Euler equations. We demonstrate that a decrease in the constraint deviation correlates with low discretization errors for all model problems, in addition to the structural advantage of ful lling the constraint.

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Section: Constraint-adapted Loss Methods (Cal)mentioning

confidence: 99%

“…which will be the constraint that a surrogate model for (21) should satisfy. As in (12) the constraint target function Φ cubic : × × , corresponding to (22), is given by…”

Section: Cubic Flux Model: Undercompressive Wavementioning

confidence: 99%