# Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks

arXiv: https://arxiv.org/abs/2202.01723 · HTML: https://mlsanity.com/paper/2202.01723/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)

## Built on by (most cited first, 23 of 23)

- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers](https://mlsanity.com/paper/2208.13273/) (2022)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration](https://mlsanity.com/paper/2409.16572/) (2024)
- [Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology](https://mlsanity.com/paper/2504.07379/) (2025)
- [Speeding up and reducing memory usage for scientific machine learning via mixed precision](https://mlsanity.com/paper/2401.16645/) (2024)
- [Deep Learning for Solving and Estimating Dynamic Macro-Finance Models](https://mlsanity.com/paper/2305.09783/) (2023)
- [Data-driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactors](https://mlsanity.com/paper/2305.03257/) (2023)
- [Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks](https://mlsanity.com/paper/2310.03001/) (2023)
- [A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoring](https://mlsanity.com/paper/2412.11967/) (2024)
- [FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design](https://mlsanity.com/paper/2505.20300/) (2025)
- [HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessment](https://mlsanity.com/paper/2408.14266/) (2024)
- [Physics Informed Constrained Learning of Dynamics from Static Data](https://mlsanity.com/paper/2504.12675/) (2025)
- [The Lost Art of Mathematical Modelling](https://mlsanity.com/paper/2301.08559/) (2023)
- [jinns: a JAX Library for Physics-Informed Neural Networks](https://mlsanity.com/paper/2412.14132/) (2024)
- [Bayesian Calibration and Model Assessment of Cell Migration Dynamics with Surrogate Model Integration](https://mlsanity.com/paper/2509.18998/) (2025)
- [Nested Fourier-enhanced neural operator for efficient modeling of radiation transfer in fires](https://mlsanity.com/paper/2604.13919/) (2026)
- [Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach](https://mlsanity.com/paper/2605.23712/) (2026)
- [Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability](https://mlsanity.com/paper/2606.12658/) (2026)
- [Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots](https://mlsanity.com/paper/2607.01749/) (2026)

## Abstract (arXiv)

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce systems-biology informed neural networks for parameter estimation by incorporating the system of ODEs into the neural networks. To complete the workflow of system identification, we also describe structural and practical identifiability analysis to analyze the identifiability of parameters. We use the ultridian endocrine model for glucose-insulin interaction as the example to demonstrate all these methods and their implementation.