This project models a genetic toggle switch, a bistable system influenced by stochastic differential equations (SDEs). The simulation incorporates Gaussian and Lévy noise, and a FCNN + Transformer model is used to estimate key parameters and predict system behavior.
The genetic toggle switch consists of two mutually repressing genes, governed by nonlinear differential equations. The system is defined by:
Stochastic Effects: Incorporates Gaussian and Lévy noise to simulate real-world randomness. Key Parameters: Includes production/degradation rates, Hill coefficient, and additional regulatory factors.
The dataset is stored in HDF5 format and contains:
U_data: Time-series data for protein U concentration. V_data: Time-series data for protein V concentration. Noise Contributions: Gaussian and Lévy noise effects. Switch Parameters: Recorded values of a, b, r, k, e per sample. 🔹 Generation Process 500 samples of simulated toggle switch trajectories. Time evolution solved numerically using Euler-Maruyama method. Stochastic noise introduced with Gaussian + Lévy processes.
The FCNN + Transformer model was trained for parameter estimation and system identification.
🔹 Components FCNN (Fully Connected Neural Network): Feature extraction from time-series data. Transformer Encoder: Captures long-range dependencies and sequential patterns. Regression Head: Outputs estimated system parameters. 🔹 Training Loss Function: Mean Squared Error (MSE) Optimizer: Adam Regularization: Early stopping based on validation loss
Model successfully learns system dynamics despite stochastic noise. Provides accurate estimations of key parameters (a, b, r, k, e). Outperforms traditional regression models on noisy datasets.
Graph Neural Networks (GNN) + Transformer for improved feature extraction. Alternative Noise Models: Studying effects of different stochastic processes. Comparisons with LSTMs and Diffusion Models for better time-series learning.