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DTSTAMP:20220812T074334Z
LOCATION:Boston 3 Room
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UID:submissions.pasc-conference.org_PASC22_sess138_msa104@linklings.com
SUMMARY:Learning Operators with Coupled Attention
DESCRIPTION:Minisymposium\n\nLearning Operators with Coupled Attention\n\n
 Kissas, Seidman, Guilhoto, Pappas, Perdikaris\n\nSupervised operator learn
 ing is an emerging machine learning paradigm with applications to modeling
  the evolution of spatio-temporal dynamical systems and approximating gene
 ral black-box relationships between functional data. We propose a novel op
 erator learning method, LOCA (Learning Operators with Coupled Attention), 
 motivated from the recent success of the attention mechanism. In our archi
 tecture, the input functions are mapped to a finite set of features which 
 are then averaged with attention weights that depend on the output query l
 ocations. By coupling these attention weights together with an integral tr
 ansform, LOCA is able to explicitly learn correlations in the target outpu
 t functions, enabling us to approximate nonlinear operators even when the 
 number of output function measurements in the training set is very small. 
 Our formulation is accompanied by rigorous approximation theoretic guarant
 ees on the universal expressiveness of the proposed model. Empirically, we
  evaluate the performance of LOCA on several operator learning scenarios i
 nvolving systems governed by ordinary and partial differential equations, 
 as well as a black-box climate prediction problem. Through these scenarios
  we demonstrate state of the art accuracy, robustness with respect to nois
 y input data, and a consistently small spread of errors over testing data 
 sets, even for out-of-distribution prediction tasks.\n\nDomain: Chemistry 
 and Materials, Computer Science and Applied Mathematics, Engineering
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