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AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification

arXiv 2310.01433 ↗First posted 29 Sep 2023q-bio.QM cs.AI cs.LGcited by 29

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Abstract (arXiv)

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model, and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. While the current work focuses on the performance of AI-Aristotle based on synthetic data, it can equally handle noisy experimental data and can even be used for black-box identification in just a few minutes on a laptop. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 23 of its 69 references that are in the map. First posted on arXiv 29 Sep 2023.

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23 of 69 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  3. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  4. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  5. 2022Symbolic Regression is NP-hardcited by 68
  6. 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
  7. 2021Optimal control of PDEs using physics-informed neural networkscited by 51
  8. 2021Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functionscited by 49
  9. 2023Interpretable Machine Learning for Science with PySR and SymbolicRegression.jlcited by 36
  10. 2022Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approachcited by 25
  11. 2023Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regressioncited by 25
  12. 2022Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networkscited by 23
11 more
  1. 2021An Approach to Symbolic Regression Using Feyncited by 20
  2. 2022Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEscited by 19
  3. 2022Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation datacited by 18
  4. 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
  5. 2018A Greedy Search Tree Heuristic for Symbolic Regressioncited by 17
  6. 2021Symbolic regression outperforms other models for small data setscited by 12
  7. 2017The Theory of Connections. Connecting Pointscited by 10
  8. 2019Partial observations and conservation laws: Grey-box modeling in biotechnology and optogeneticscited by 9
  9. 2023Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel enginescited by 6
  10. 2022Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systemscited by 5
  11. 2023Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron modelscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 12; 2025: 9; 2026: 7.

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  1. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  2. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  3. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 10
  4. 2025A Neural Symbolic Model for Space Physicscited by 10
  5. 2025Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacologycited by 10
  6. 2023AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regressioncited by 9
  7. 2024Nonlinear Discrete-Time Observers with Physics-Informed Neural Networkscited by 8
  8. 2024Physics-Informed Neural Networks and Extensionscited by 8
  9. 2024GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Lawscited by 8
  10. 2024CMINNs: Compartment Model Informed Neural Networks -- Unlocking Drug Dynamicscited by 7
  11. 2026Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelinescited by 6
  12. 2024Adapting Physics-Informed Neural Networks to Improve ODE Optimization in Mosquito Population Dynamicscited by 4
17 more
  1. 2025Physics-Informed Machine Learning in Biomedical Science and Engineeringcited by 4
  2. 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiologycited by 3
  3. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3
  4. 2025DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraintscited by 3
  5. 2024A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEscited by 2
  6. 2025FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor designcited by 2
  7. 2025Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learningcited by 2
  8. 2025Learning Coupled System Dynamics under Incomplete Physical Constraints and Missing Datacited by 2
  9. 2025Physics Informed Constrained Learning of Dynamics from Static Datacited by 1
  10. 2026Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEscited by 1
  11. 2024About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networkscited by 0
  12. 2025CBINNS: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identificationcited by 0
  13. 2026Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approachcited by 0
  14. 2026Meta-Inverse Physics-Informed Neural Networks for High-Dimensional Ordinary Differential Equationscited by 0
  15. 2026Learning dynamical systems with biochemically informed neural ordinary differential equationscited by 0
  16. 2026Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiabilitycited by 0
  17. 2026Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equationscited by 0