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Abstract We present a probabilistic extension of action language $${\cal BC}$$+$$ . Just like $${\cal BC}$$+$$ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call p $${\cal BC}$$+$$ , is defined as a high-level notation of LP MLN programs—a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in p $${\cal BC}$$+$$ and computed using an implementation of LP MLN .
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Deep level-set method for Stefan problems
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a feed-forward neural network, whose parameters are trained using the probabilistic formulation of the Stefan growth condition. The algorithm can handle Stefan problems where the liquid is supercooled and can capture surface tension effects through the simulation of particles along the moving boundary together with an efficient approximation of the mean curvature. We demonstrate the effectiveness of the method on a variety of examples with and without radial symmetry.
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- Award ID(s):
- 2108680
- PAR ID:
- 10519297
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Computational Physics
- Volume:
- 503
- Issue:
- C
- ISSN:
- 0021-9991
- Page Range / eLocation ID:
- 112828
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jcp.2024.112828
