[논문 리뷰] Learning to control non-equilibrium dynamics using local imperfect gradients

Carlos Floyd, Aaron R. Dinner외 1명|arXiv (Cornell University)|2024. 04. 04.

Model Reduction and Neural Networks인용 수 5

한 줄 요약

The paper proposes spatiotemporally local, imperfect feedback rules to learn driving protocols that steer non-equilibrium dynamics, for both conservative and non-conservative systems, with several physical exemplars.

ABSTRACT

Standard approaches to controlling dynamical systems involve biologically implausible steps such as backpropagation of errors or intermediate model-based system representations. Recent advances in machine learning have shown that "imperfect" feedback of errors during training can yield test performance that is similar to using full backpropagated errors, provided that the two error signals are at least somewhat aligned. Inspired by such methods, we introduce an iterative, spatiotemporally local protocol to learn driving forces and control non-equilibrium dynamical systems using imperfect feedback signals. We present numerical experiments and theoretical justification for several examples. For systems in conservative force fields that are driven by external time-dependent protocols, our update rules resemble a dynamical version of contrastive divergence. We appeal to linear response theory to establish that our imperfect update rules are locally convergent for these conservative systems. Finally, we show that similar local update rules can also solve dynamical control problems for non-conservative systems, and we illustrate this in the non-trivial example of active nematics. Our updates allow learning spatiotemporal activity fields that pull topological defects along desired trajectories in the active nematic fluid. These imperfect feedback methods are information efficient and in principle biologically plausible, and they can help extend recent methods of decentralized training for physical materials into dynamical settings.

연구 동기 및 목표

• Motivate biologically plausible, locally computable learning rules for guiding non-equilibrium trajectories.
• Develop and analyze imperfect update rules that approximate non-local optimal control gradients.
• Show convergence and effectiveness across conservative and non-conservative dynamical systems.
• Demonstrate applicability to concrete physical models such as beads in time-dependent traps, membranes, reaction networks, and active nematics.

제안 방법

• Introduce temporally local learning rules that update driving protocols using only present-time observables.
• Use imperfect gradients that distort true gradients with fixed positive-definite matrices and prove convergence under certain conditions.
• Derive a non-equilibrium extension of gradient-based learning for conservative systems via a quasi-static reduction to equilibrium gradients.
• Derive a monotonic update rule for steady-state control in non-conservative Markov networks based on sign-consistent partial derivatives.
• Apply the update rules to a bead in a moving potential, a Helfrich membrane with spontaneous curvature, a driven chemical network, and an active nematic fluid.

실험 결과

연구 질문

• RQ1 Can locally accessible, imperfect gradient signals guide non-equilibrium trajectories toward a target dynamical path?
• RQ2 Under what conditions do distorted local updates still converge to the desired trajectory in conservative dynamics?
• RQ3 How can local learning rules be extended to control non-conservative systems and steady-state distributions?
• RQ4 Do local updates suffice to steer complex active matter systems, such as active nematics, toward specified defect trajectories?

주요 결과

• Imperfect, spatiotemporally local updates converge to target trajectories in Markov chain dynamics, even when error signals are distorted.
• For conservative, non-autonomous systems, quasi-static reductions enable using equilibrium gradients to guide learning with convergence supported by linear response concepts.
• A simple local update based on the difference in free energy density can steer non-equilibrium steady states toward targets in non-conservative systems.
• Local update rules can drive defect trajectories in active nematics, demonstrating applicability to complex, non-equilibrium materials.
• Distortions in the gradient affect convergence rates but not the fixed points, under specified conditions (positive eigenvalues or positive definiteness).
• The learning framework is information-efficient and potentially biologically plausible, enabling decentralized training in dynamical settings.