Flow SDE for Learning System Dynamics

This project explores advanced techniques for estimating energy landscapes and modeling dynamic systems using force and potential models. It further provides indicators for state transitions.

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Key Features

1. Dynamic System Modeling:

   • Estimation of energy landscapes (force + potential).
   • Learning equilibrium and non-equilibrium dynamics.
   • Combining EPR loss and HJB loss for potential optimization.

2. State Transition Analysis:

   • Using energy landscapes to identify tipping points and state transitions.

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Source Code Overview

1. Simulation of Transitions

Simulated Data with Julia

• Maier-Stein Model:

  • Simulates transitions between fixed points.
  • Run with Julia:

    julia --threads 20 MaierStein.jl

• Epileptor Model:

  • Simulates transitions between fixed points.
  • Run with Julia:

    julia --threads 20 Epileptor_sde.jl

• FitzHugh-Nagumo Model:

  • Simulates dynamic systems with state transitions.
  • Run with Julia:

    julia --threads 20 FitzHughNagumo.jl

Open Dataset

• Muller-Brown Potential:
  • Based on the dataset from msmbuilder.

Simulated Data with Python

• Two-Well System:

  • Dataset from EPR-Net repository.

• Lorenz System:

  • Dataset from EPR-Net repository.

• 12D Gaussian Mixture Model (GMM):

  • Dataset from EPR-Net repository.

• Epilepsy Data:

  • Based on the non-equilibrium indicator paper: PhysRevE.

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2. Model Configurations

Six different model settings are available for experimentation:

1. only_force: Force model.
2. potential: Force model + potential model.
3. bridge: Bridge model with force learning.
4. bridge_potential: Bridge model + force model + potential model.

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3. Training Modes

2D Experiments

Choose from various datasets and modes for training:

• Example command:

  python exp_0_2d_force_potential_bridge_train_test.py \
      dataset=fhn \                   # Dataset: fhn/msn/mbn/two_well
      mode=${m} \                     # Training mode: only_force/potential/bridge/bridge_score/bridge_potential/bridge_potential_score
      mode.rho_epr=${rho_epr} \       # Weight for EPR loss (for potential model optimization)
      mode.rho_hjb=${rho_hjb} \       # Weight for HJB loss (for potential model optimization)
      gpu_id=0 \                        # GPU ID
      downsample_ratio=4   \             # saving time
      bridge_type=exact   \           # choose brdige type: schrondinger / exact