zinoex/hyperverlet

hyperverlet's Issues

Fix bib

Ablation studies

• Placement of hypersolver
  • solver dp dq dp
  • dp solver dq solver dp solver
  • dq
  • dp
  • dq and dp
• Combined model/Seperate model
• Model input
  • dp, dq, m, extra_args
  • p, q, dp, dq, m, extra_args
  • dp, dq, t, dt, m, extra_args
  • dp, dq, dp_pre, dq_pre, m, extra_args
• Loss function
  • Residual
  • Trajectory
  • Time decay
  • L1 vs L2 loss

Test and tune 3-body spring mass system

Neural network for Lennard Jones

Visualization of spring mass system

ctrl + f checks

• hypsersolver - small capitalization for the class hypersolvers
• HyperVerlet
• HyperEuler
• HyperHeun
• velocity Verlet

Adversarial paper from Bin

Look into the paper sent by Bin, and try to see if it can prevent accumulation of errors.

Potentially after submission.

Momentum plot

Master Thesis sections

• Summery
• Abstract
• Preface
• Introduction
• Theory
  • Mechanics
    • Newtonian
    • Lagrangian
    • Hamiltonian
  • Integrator
    • Truncation Error
    • Euler
    • Heun
    • RK4
    • Velocity Verlet
    • Forest-Ruth
• Related Works
  • ML for physical simulations
    • GNS
    • Learning Lagrangian Fluid Dynamics with Graph Neural Networks (FGN)
    • Machine Learning accelerated Computational Fluid Dynamics
    • Adaptive machine learning framework to accelerate ab initio molecular dynamics
    • JAX-MD
    • TorchMD: A deep learning framework for molecular simulations
  • Neural ODE
    • Neural ODE
    • Latent ODEs for Irregularly-Sampled Time Series
    • Latent SDE
    • Graph NeuralODE
    • Learning differential equations that are easy to solve
  • Symplectic Neural Networks
    • Variational Integrator Networks for Physically Structured Embeddings
    • Symplectic Recurrent Neural Networks
    • Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems, about symmetric and symplectic Taylor series
    • Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
    • Hamiltonian Neural Networks for solving differential equations
  • Physics inspired optimization
    • A variational perspective on accelerated methods in optimization
    • Dynamical, Symplectic and Stochastic Perspectives on Gradient-Based Optimization
    • On Dissipative Symplectic Integration with Applications to Gradient-Based Optimization
  • Deep integrators
    • Deep Euler Method
    • Hyper euler / Hyper huen
• Method
  • Velocity verlet + hypersolver = hyperverlet
  • Predictor-corrector architecture
  • Residual training for VV
  • Desirable properties of the NN
• Experiment systems
  • Pendulum
  • Spring mass
  • 3-body spring mass
• Results
  • Integrator comparison
    • Spring mass
    • Pendulum
    • Three body spring mass
  • Ablation study
    • Underlying model type (for multibody systems)
    • Underlying model size (show no overfitting)
    • Apply NN between VV-steps or after
    • Delta T power (including not multiplying by Delta T)
  • Generalization study
    • Train duration
    • Variable parameters
    • Out of distribution
• Discussion
• Conclusion

Updater figure med respect til dt \macro

Regularization

BatchNorm or something

Ideas for extensions for the exam

Generalization studies

• Out-of-distribution
• Variable parameters
• Train duration stddev
• Stiff system (high initial momentum)

Pytorch dataset for LAMMPS Lennard-Jones data

The bla bla in between

• Preface
• Summery
• Abstract
• Title

3-body spring mass system model