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Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

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Angeliki Koutsimpela, Michail Loulakis

Optimization and Control · Submitted 15 Jan 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems.

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arXiv ID2401.07642 (version 1)
Pith IDYQOGACQF, Pith's permanent record of this paper and its review
CitationAngeliki Koutsimpela, Michail Loulakis. "Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem." arXiv:2401.07642 (2024). https://pith.science/paper/YQOGACQF
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,344 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.12 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake problem.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. result 0.63 0.96 0.69 asserted 1.00
s1 We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake problem. contribution 0.50 0.96 0.23 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake problem.

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