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Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to…

Machine Learning · Computer Science 2022-09-07 Daniel M. DiPietro , Bo Zhu

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of…

Machine Learning · Computer Science 2023-04-21 Tommaso Bendinelli , Luca Biggio , Pierre-Alexandre Kamienny

This tutorial paper provides a general overview of symbolic regression (SR) with specific focus on standards of interpretability. We posit that interpretable modeling, although its definition is still disputed in the literature, is a…

Machine Learning · Computer Science 2023-06-02 Jennifer J. Schnur , Nitesh V. Chawla

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…

Computational Physics · Physics 2020-04-16 Silviu-Marian Udrescu , Max Tegmark

Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…

Machine Learning · Computer Science 2021-10-27 Ismail Alaoui Abdellaoui , Siamak Mehrkanoon

Accurate estimation of the Q-function is a central challenge in offline reinforcement learning. However, existing approaches often rely on a shared global Q-function, which is inadequate for capturing the compositional structure of tasks…

Machine Learning · Computer Science 2026-03-19 Qiushui Xu , Yuhao Huang , Yushu Jiang , Lei Song , Jinyu Wang , Wenliang Zheng , Jiang Bian

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…

Machine Learning · Computer Science 2020-04-28 J. Kubalík , E. Derner , R. Babuška

Reinforcement learning (RL) for continuous control often requires large amounts of online interaction data. Value-based RL methods can mitigate this burden by offering relatively high sample efficiency. Some studies further enhance sample…

Machine Learning · Computer Science 2025-05-30 Jijia Liu , Feng Gao , Qingmin Liao , Chao Yu , Yu Wang

Semantic communication (SemCom) is an emerging paradigm that leverages semantic-level understanding to improve communication efficiency, particularly in resource-constrained scenarios. However, existing SemCom systems often overlook diverse…

Networking and Internet Architecture · Computer Science 2025-06-25 Xinyi Lin , Peizheng Li , Adnan Aijaz

Developing mathematical models of dynamic systems is central to many disciplines of engineering and science. Models facilitate simulations, analysis of the system's behavior, decision making and design of automatic control algorithms. Even…

Machine Learning · Computer Science 2020-06-19 Erik Derner , Jiří Kubalík , Nicola Ancona , Robert Babuška

In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features…

Machine Learning · Computer Science 2024-06-18 Assaf Shmuel , Oren Glickman , Teddy Lazebnik

We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM…

Machine Learning · Computer Science 2025-07-10 M. A. Evangelista-Alvarado , P. Suárez-Serrato

We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…

Machine Learning · Computer Science 2026-03-30 Zachary Bastiani , Robert M. Kirby , Jacob Hochhalter , Shandian Zhe

The discovery of constitutive laws for complex materials has historically faced a dichotomy between high-fidelity data-driven approaches, which demand prohibitive full-field experimental data, and traditional engineering fitting, which…

Computational Engineering, Finance, and Science · Computer Science 2026-03-23 Yue Wu , Tianhao Su , Mingchuan Zhao , Shunbo Hu , Deng Pan

Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…

Machine Learning · Computer Science 2026-03-31 Viktor Martinek , Roland Herzog

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

Machine Learning · Computer Science 2025-06-25 Paul Kahlmeyer , Joachim Giesen , Michael Habeck , Henrik Voigt

We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as…

Machine Learning · Computer Science 2026-02-04 Yesom Park , Annie C. Lu , Shao-Ching Huang , Qiyang Hu , Y. Sungtaek Ju , Stanley Osher

Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data. Most existing SR methods function within a bi-level optimization framework: an outer loop that…

Machine Learning · Computer Science 2026-05-25 Boxiao Wang , Kai Li , Zhiwei Chen , Yang Huang , Runxiang Wang , Ziwen Zhang , Yifan Zhang , Jian Cheng

Sample efficiency is critical when applying learning-based methods to robotic manipulation due to the high cost of collecting expert demonstrations and the challenges of on-robot policy learning through online Reinforcement Learning (RL).…

Machine Learning · Computer Science 2024-06-21 Arsh Tangri , Ondrej Biza , Dian Wang , David Klee , Owen Howell , Robert Platt

In Reinforcement Learning (RL), training a policy from scratch with online experiences can be inefficient because of the difficulties in exploration. Recently, offline RL provides a promising solution by giving an initialized offline…

Machine Learning · Computer Science 2024-05-14 Changhong Wang , Xudong Yu , Chenjia Bai , Qiaosheng Zhang , Zhen Wang
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