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Linearly Constrained Neural Networks
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We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear transformation of an underlying potential field, which is in turn modelled by a neural network. This transformation is chosen such that any prediction of the target function is guaranteed to satisfy the constraints. The approach is demonstrated on both simulated and real data examples.
Forward citations
Cited by 3 Pith papers
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Steering Neural Network Training through Interpretable Constraints Based on Partial Dependence
Constraining neural network partial dependence to match domain-knowledge functional forms during training improves predictive accuracy, data efficiency, and explanation faithfulness on regression problems.
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Deep Generative Models with Hard Linear Equality Constraints
Conditioning the Gaussian latent or output distribution of a deep generative model on a linear equality constraint, with the conditional mean as the gradient proxy, enforces the constraint exactly and improves generat...
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Meta-Learning for Physically-Constrained Neural System Identification
Gradient-based meta-learning over neural state-space models adapts a model to a new dynamical system with little target data and few gradient steps, with physical constraints embedded in the architecture.
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