CSSV-NNs and inc-CSSV-NNs provide universal approximation of frame-indifferent isotropic polyconvex hyperelastic energies, showing Ball's criterion is sufficient but not necessary.
Optimal Control Via Neural Networks: A Convex Approach
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
Control of complex systems involves both system identification and controller design. Deep neural networks have proven to be successful in many identification tasks, however, from model-based control perspective, these networks are difficult to work with because they are typically nonlinear and nonconvex. Therefore many systems are still identified and controlled based on simple linear models despite their poor representation capability. In this paper we bridge the gap between model accuracy and control tractability faced by neural networks, by explicitly constructing networks that are convex with respect to their inputs. We show that these input convex networks can be trained to obtain accurate models of complex physical systems. In particular, we design input convex recurrent neural networks to capture temporal behavior of dynamical systems. Then optimal controllers can be achieved via solving a convex model predictive control problem. Experiment results demonstrate the good potential of the proposed input convex neural network based approach in a variety of control applications. In particular we show that in the MuJoCo locomotion tasks, we could achieve over 10% higher performance using 5* less time compared with state-of-the-art model-based reinforcement learning method; and in the building HVAC control example, our method achieved up to 20% energy reduction compared with classic linear models.
representative citing papers
Input-convex neural networks in elementary polynomials of signed singular values provably approximate any frame-indifferent isotropic polyconvex hyperelastic energy.
HyCNNs are a new architecture that learns convex functions with exponentially fewer parameters than ICNNs and outperforms them in convex regression and high-dimensional optimal transport on synthetic and single-cell RNA data.
A new differentiable layer with convex parameter space universally approximates generalized convex functions and their gradients, enabling single-level reformulations of bilevel problems in optimal transport and multi-good auctions.
Framework with MPC-aware feature selection, Input-Convex Encoder-Only Transformer, and ADMM achieves near-centralized performance in scalable distributed MPC for heterogeneous building aggregations.
CCEM parameterizes compositional energy factors with input-convex neural networks and optimizes over a convex relaxation to enable deterministic scaling from small to large combinatorial reasoning instances.
citing papers explorer
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Modeling isotropic polyconvex hyperelasticity by neural networks -- sufficient and necessary criteria for compressible and incompressible materials
CSSV-NNs and inc-CSSV-NNs provide universal approximation of frame-indifferent isotropic polyconvex hyperelastic energies, showing Ball's criterion is sufficient but not necessary.
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Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies
Input-convex neural networks in elementary polynomials of signed singular values provably approximate any frame-indifferent isotropic polyconvex hyperelastic energy.
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Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
HyCNNs are a new architecture that learns convex functions with exponentially fewer parameters than ICNNs and outperforms them in convex regression and high-dimensional optimal transport on synthetic and single-cell RNA data.
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Universal Representation of Generalized Convex Functions and their Gradients
A new differentiable layer with convex parameter space universally approximates generalized convex functions and their gradients, enabling single-level reformulations of bilevel problems in optimal transport and multi-good auctions.
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A Data-Driven Methodology for Scalable Distributed MPC in Heterogeneous Building Aggregation: From Systematic Feature Selection to Convex Optimization
Framework with MPC-aware feature selection, Input-Convex Encoder-Only Transformer, and ADMM achieves near-centralized performance in scalable distributed MPC for heterogeneous building aggregations.
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Convex Compositional Reasoning Models
CCEM parameterizes compositional energy factors with input-convex neural networks and optimizes over a convex relaxation to enable deterministic scaling from small to large combinatorial reasoning instances.