Learning Symbolic Physics with Graph Networks

By Miles Cranmer, Rui Xu, Peter W. Battaglia, Shirley Ho. 2019

99 citations recorded by the source corpus.

We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.

Subfields: Artificial Intelligence, Graph Learning, Signal Processing

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Citations in the corpus

The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence (2020, background): “…in multiple domains, as depicted in Figure 5: current neural networks lack explicit mechanisms for these forms of reasoning, and lack natural ways of representing and reasoning over such domains (but see e.g., Cranmer et al., 2019) Compare the gist of these two figures with current trends.”
Graph Neural Networks with Learnable Structural and Positional Representations (2021, background): “, 2021), physics (Cranmer et al., 2019; Bapst et al., 2020), combinatorial optimization (Bengio et al.”
Graph neural networks in particle physics (2020, background): “Inspired by the success deep learning has achieved at reaching super-human performance at various tasks, various domains in the physical sciences [2], including particle physics [1, 3–6], have begun exploring deep learning as a unique tool for handling difficult scientific problems that go beyond st”
Benchmarking Graph Neural Networks (2023, background): “, 2017), physics (Cranmer et al., 2019; Sanchez-Gonzalez et al., 2020), social sciences (Kipf and Welling, 2017; Monti et al.”
Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, background): “Our work is a generalized and extended version of that in [5].”
A Generalization of Transformer Networks to Graphs (2020, background): “…network architectures on graph datasets and have achieved signiﬁcant success on a wide range of applications, such as in knowledge graphs (Schlichtkrull et al. 2018; Chami et al. 2020), in social sciences (Monti et al. 2019), in physics (Cranmer et al. 2019; Sanchez-Gonzalez et al. 2020), etc.”