Machine Learning, Dynamical Systems and Control



Our goal is to specifically learn physically interpretable models of dynamical systems from off-line and/or on-line streaming data. Physics informed learning is of growing importance for scientific and engineering problems. Physics informed simply refers to our ability to constrain the learning process by physical and/or engineering principles. For instance, conservation of mass, momentum, or energy can be imposed in the learning process. In the parlance of ML, the imposed constraints are referred to as regularizers. Thus, physics informed learning focuses on adding regularization to the learning process to impose or enforce physical priors. There are four major stages in machine learning: 1) determining a high- level task or objective, 2) collecting and curating the training data, 3) identifying the model architecture and parameterization, and 4) choosing an optimization strategy to determine the parameters of the model from the data. Known physics (e.g., invariances, symmetries, conservation laws, constraints, etc.) may be incorporated in each of these stages. For example, rotational invariance is often incorporated by augment- ing the training data with rotated copies, and translational invariance is often captured using convolutional neural network architectures. In kernel-based techniques, such as Gaussian process regression and sup- port vector machines, symmetries can be imposed by means of rotation-invariant, translation-invariant, and symmetric covariance kernels. Additional physics and prior knowledge may be incorporated as additional loss functions or constraints in the optimization problem.




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Hod Lipson, Professor
Thrust Co-Lead: AI for Modeling
Columbia University
Website: [ VIEW ]
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Scott McCalla, Assistant Professor
Thrust Co-Lead: AI for Modeling
Montana State University
Website: [ VIEW ]




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