arXiv subjects

Sergei Garmaev

Publications and source records attributed to Sergei Garmaev.

5 recordsLinked to original sources

arXiv2026

A Data-Free Symbolic Regression Approach for Solving Equations

Many equations arising in science currently cannot be solved by available analytical techniques and are therefore solved numerically, without yielding explicit symbolic expressions. Existing symbolic regression approaches can recover symbolic expressions, but require training data obtained from the underlying process, rather than the governing equation alone. We propose the Symbolic Equation Solver (SES), a framework that formulates equation solving as an optimization problem over differentiable symbolic models. SES constructs its objective from the equation together with initial or boundary conditions, eliminating the need for paired input-output data. The learned model is expressed in explicit symbolic form, enabling further analysis. We evaluate SES on representative algebraic and differential equations, including a system of algebraic equations, an equation with transcendental terms, an ordinary differential equation, and partial differential equations with different initial or boundary conditions. Across these settings, SES recovers compact symbolic expressions that match the corresponding analytical solutions.

cs.NE↗

arXiv2026

Complex Equation Learner: Rational Symbolic Regression with Gradient Descent in Complex Domain

Symbolic regression aims to discover interpretable equations from data, yet modern gradient-based methods fail for operators that introduce singularities or domain constraints, including division, logarithms, and square roots. As a result, Equation Learner-type models typically avoid these operators or impose restrictions, e.g. constraining denominators to prevent poles, which narrows the hypothesis class. We propose a complex weight extension of the Equation Learner that mitigates real-valued optimization pathologies by allowing optimization trajectories to bypass real-axis degeneracies. The proposed approach converges stably even when the target expression has real-domain poles, and it enables unconstrained use of operations such as logarithm and square root. We Validate the method on symbolic regression benchmarks and show it can recover singular behavior from experimental frequency response data.

cs.LG↗

arXiv2025

From Physics to Machine Learning and Back: Part II - Learning and Observational Bias in PHM

Prognostics and Health Management ensures the reliability, safety, and efficiency of complex engineered systems by enabling fault detection, anticipating equipment failures, and optimizing maintenance activities throughout an asset lifecycle. However, real-world PHM presents persistent challenges: sensor data is often noisy or incomplete, available labels are limited, and degradation behaviors and system interdependencies can be highly complex and nonlinear. Physics-informed machine learning has emerged as a promising approach to address these limitations by embedding physical knowledge into data-driven models. This review examines how incorporating learning and observational biases through physics-informed modeling and data strategies can guide models toward physically consistent and reliable predictions. Learning biases embed physical constraints into model training through physics-informed loss functions and governing equations, or by incorporating properties like monotonicity. Observational biases influence data selection and synthesis to ensure models capture realistic system behavior through virtual sensing for estimating unmeasured states, physics-based simulation for data augmentation, and multi-sensor fusion strategies. The review then examines how these approaches enable the transition from passive prediction to active decision-making through reinforcement learning, which allows agents to learn maintenance policies that respect physical constraints while optimizing operational objectives. This closes the loop between model-based predictions, simulation, and actual system operation, empowering adaptive decision-making. Finally, the review addresses the critical challenge of scaling PHM solutions from individual assets to fleet-wide deployment. Fast adaptation methods including meta-learning and few-shot learning are reviewed alongside domain generalization techniques ...

cs.LG↗

arXiv2025

A Neural Operator-Based Approach to Symbolic Discovery of PDEs

Discovering governing equations from data remains challenging when the underlying dynamics involve nonlocal differential operators, field interactions governed by auxiliary equations, or temporal memory effects. We propose Neural Operator-based symbolic Model approximaTion and discOvery (NOMTO), a framework that extends Equation Learner-type symbolic architectures by incorporating pretrained neural operators as nodes in the symbolic network. NOMTO represents candidate equations as sparse differentiable computational graphs that combine algebraic operations with fixed neural operator surrogates pretrained to approximate nonlinear operators. We evaluate the method on model-discovery problems involving nonlocal spatial operators, couplings mediated by auxiliary field equations, and temporal integral terms representing memory effects. The results show that NOMTO can recover compact governing equations containing nonlocal operator terms, thereby extending symbolic model discovery beyond libraries restricted to local derivatives and point-wise algebraic combinations.

cs.AI↗

arXiv2023

Deep Koopman Operator-based degradation modelling

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion for reliable health indicators is their capability to discern a degradation trend. However, trending can pose challenges due to the variability of operating conditions. An optimal transformation of health indicators would therefore be one that converts degradation dynamics into a coordinate system where degradation trends exhibit linearity. Koopman theory framework is well-suited to address these challenges. In this work, we demonstrate the successful extension of the previously proposed Deep Koopman Operator approach to learn the dynamics of industrial systems by transforming them into linearized coordinate systems, resulting in a latent representation that provides sufficient information for estimating the system's remaining useful life. Additionally, we propose a novel Koopman-Inspired Degradation Model for degradation modelling of dynamical systems with control. The proposed approach effectively disentangles the impact of degradation and imposed control on the latent dynamics. The algorithm consistently outperforms in predicting the remaining useful life of CNC milling machine cutters and Li-ion batteries, whether operated under constant and varying current loads. Furthermore, we highlight the utility of learned Koopman-inspired degradation operators analyzing the influence of imposed control on the system's health state.

eess.SY↗