Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery

• URL: http://arxiv.org/abs/2306.17038v1
• Date: Thu, 29 Jun 2023 15:37:19 GMT
• Title: Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery
• Authors: Mikhail Maslyaev and Alexander Hvatov
• Abstract summary: Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.
• Score: 77.34726150561087
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizational problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.

Related papers

• Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations [0.0]
  We propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms. We perform numerical simulations of these equations to demonstrate their validity as accurate approximations of the original algorithms.
  arXiv  Detail & Related papers  (2024-11-14T19:00:01Z)
• An Inexact Halpern Iteration with Application to Distributionally Robust Optimization [9.529117276663431]
  We investigate the inexact variants of the scheme in both deterministic and deterministic convergence settings. We show that by choosing the inexactness appropriately, the inexact schemes admit an $O(k-1) convergence rate in terms of the (expected) residue norm.
  arXiv  Detail & Related papers  (2024-02-08T20:12:47Z)
• Convex Q Learning in a Stochastic Environment: Extended Version [1.680268810119084]
  The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The proposed algorithms are convergent and new techniques are introduced to obtain the rate of convergence in a mean-square sense. The theory is illustrated with an application to a classical inventory control problem.
  arXiv  Detail & Related papers  (2023-09-10T18:24:43Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Efficient Alternating Minimization Solvers for Wyner Multi-View Unsupervised Learning [0.0]
  We propose two novel formulations that enable the development of computational efficient solvers based the alternating principle. The proposed solvers offer computational efficiency, theoretical convergence guarantees, local minima complexity with the number of views, and exceptional accuracy as compared with the state-of-the-art techniques.
  arXiv  Detail & Related papers  (2023-03-28T10:17:51Z)
• Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
  Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations. We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
  arXiv  Detail & Related papers  (2022-10-15T17:32:49Z)
• Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equations [83.3201889218775]
  Several widely-used first-order saddle-point optimization methods yield an identical continuous-time ordinary differential equation (ODE) when derived naively. However, the convergence properties of these methods are qualitatively different, even on simple bilinear games. We adopt a framework studied in fluid dynamics to design differential equation models for several saddle-point optimization methods.
  arXiv  Detail & Related papers  (2021-12-27T18:31:34Z)
• Optimal oracle inequalities for solving projected fixed-point equations [53.31620399640334]
  We study methods that use a collection of random observations to compute approximate solutions by searching over a known low-dimensional subspace of the Hilbert space. We show how our results precisely characterize the error of a class of temporal difference learning methods for the policy evaluation problem with linear function approximation.
  arXiv  Detail & Related papers  (2020-12-09T20:19:32Z)
• The data-driven physical-based equations discovery using evolutionary approach [77.34726150561087]
  We describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
  arXiv  Detail & Related papers  (2020-04-03T17:21:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.