ODE Solving

ODE: Ordinary Differential Equation

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8 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Boosted Physics-Informed Neural Networks for Solving Homogeneous and Non-Homogeneous Lane-Emden Type Equations
Oct 31, 2026Luke Oluwaseye JoelODE Solving Physics-Informed ML
Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa
Ghost tasking for parametrized Gaussian Processes solving linear differential equations
Oct 8, 2026Johanna Moser, Christopher Albert, Sascha RanftlODE Solving Gaussian Processes
GRADSOLVE: fast exact gradients for ODE ensembles on GPUs
Sep 2, 2026Alessio Spurio ManciniODE Solving GPU Acceleration
Department of Physical Sciences and Engineering, Royal Holloway, University of London, Egham Hill, Egham TW20 0EX, United Kingdom
DeSyR: A decoupled symbolic recovery framework for PDEs with PINN-guided structure discovery and physics-based coefficient refinement
Sep 1, 2026Pancheng Niu, Jun Guo, Qiaolin He +2Parameter Estimation ODE Solving
Chengdu University of Information Technology, College of Applied Mathematics, Chengdu, 610225, China · Sichuan University, School of Mathematics, Chengdu, 610065, China · Hong Kong Polytechnic University, Department of Computing, Hong Kong, 999077, China +1
Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations
Aug 27, 2026Yuehao Song, Zhong Chen, Lihui Cen +2ODE Solving Physics-Informed ML
School of Automation, Central South University, Changsha, China · School of Automation, Central South University, 932 South Lushan Road, Changsha 410083, China · Johns Hopkins University, Baltimore, USA +3
Modern analog computing for solving differential and matrix equations
Jun 11, 2026Zhong Sun, Piergiulio Mannocci, Manuel Le Gallo +1Analog Computing ODE Solving
Institute for Artificial Intelligence, School of Integrated Circuits, Peking University, Beijing Advanced Innovation Center for Integrated Circuits, Beijing 100871, China. · 2Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, 20133, Italy. · 3IBM Research Europe, Rüschlikon, Switzerland.
Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
Jun 6, 2026Nathanael BoschDynamical Systems Uncertainty Quantification
EPFL, Lausanne, Switzerland
Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals
May 25, 2026Munawar Ali, Qi Feng, Charlie Pyle +1ODE Solving Kernel Methods
Department of Mathematics, Florida State University, Tallahassee, FL 32306 · Department of Mathematics, Texas A&M University, College Station, TX 77843 · Department of Mathematics, Rutgers University, Piscataway, NJ 08854

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Boosted Physics-Informed Neural Networks for Solving Homogeneous and Non-Homogeneous Lane-Emden Type Equations

Luke Oluwaseye Joel

Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa

ODE Solving Physics-Informed ML

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The Lane-Emden Equation is a class of nonlinear differential equations commonly used to model phenomena in astrophysics and mathematical physics, such as stellar structure and thermal behavior in polytropic gas spheres. This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations. Standard PINNs leverage physical laws encoded within the loss function, but their predictive performance can be constrained by optimization challenges and approximation errors. To address this, we introduce a post-processing boosting stage where the residual errors from the PINN prediction are modeled using some regression algorithms - including LightGBM, Random Forest, XGBoost, and Support Vector Regression (SVR). The outputs from these boosted models are aggregated to generate a corrected, high-fidelity prediction. The proposed methodology is systematically validated through quantitative metrics and comparative analysis against the standard PINN baseline. The results demonstrate that the boosted PINN framework significantly reduces prediction error, and improves generalization, offering a powerful and flexible approach for solving scientific and engineering problems governed by differential equations.