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Neural Network Reparametrization for Accelerated Optimization in Molecular Simulations
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Proposes neural network reparametrization of molecular degrees of freedom, using a GNN whose graph is built from slow Hessian modes, to accelerate energy minimization without force-matching or back-mapping.
Problem
Energy minimization in molecular simulations is slow because of disparate curvature scales (stiff bonds vs weak van der Waals), and conventional coarse-graining requires force-matching and back-mapping.
Approach
Reparametrize fine-grained coordinates as a (possibly overparametrized) neural function of latent coordinates, using a GNN whose adjacency is the projection onto slow Hessian modes (a canonical Hessian backbone of Laplacian form), so the optimizer moves slow directions faster and tolerates larger learning rates.
Key results
- On the pure Lennard-Jones loop, the GNN reparametrization is the only method that finds the correct loop layout, while plain GD mostly leaves some nodes far away.
- On protein folding, GNN models reach lower energies than the GD baseline with speedups across six proteins, but in most cases OpenMM reaches deeper RMSD minima.
- GNN runs at 3-5k steps reach energies close to 10k-step OpenMM runs on 2JOF, though OpenMM takes less wall-clock time.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GNN reparametrization instead of direct gradient descent | Molecular energy minimization · Pure LJ loop | energy | Helped |
| Use GNN reparametrization instead of linear CG reparametrization | Molecular energy minimization · Pure LJ loop | energy | Helped |
| Use CG reparametrization instead of direct gradient descent | Molecular energy minimization · Pure LJ loop | energy | Helped |
| Use GNN reparametrization instead of direct gradient descent | Molecular energy minimization · Bond+LJ loop | convergence speed | Helped |
| Use CG reparametrization instead of direct gradient descent | Molecular energy minimization · Bond+LJ loop | energy | Helped |
| Use GNN reparametrization instead of the baseline | Protein folding · Selected proteins | runtime | Helped |
| Use GNN reparametrization instead of direct gradient descent | Protein folding · Selected proteins | energy | Mixed |
| Use GNN reparametrization instead of OpenMM | Protein folding · 2JOF | energy | Helped |
| Use GNN reparametrization instead of OpenMM | Protein folding · 2JOF | runtime | Hurt |
| Use GNN reparametrization instead of OpenMM | Protein folding · 2JOF | RMSD | Hurt |
| Use two GCN layers instead of one (ablation) | GNN reparametrization · 2JOF | energy | No clear effect |
| Vary GNN hidden dimension (ablation) | GNN reparametrization · 2JOF | RMSD | No clear effect |
Surprising findings
- The GNN-based models sometimes reach higher final energy than OpenMM but still achieve a lower RMSD, showing energy and structural quality can disagree.
- OpenMM is faster in wall-clock time than the authors' implementation despite the reparametrization gains in steps.
Limitations
- Wall-clock time is worse than OpenMM despite fewer optimization steps; implementation is not optimized.
- Protein experiments use a simplified implicit-solvent force field and small proteins; OpenMM often reaches deeper RMSD minima.
- The slow-mode robustness argument relies on random-matrix heuristics and assumptions about weight distributions.
Experimental setup
Datasets: synthetic loop systems (Lennard-Jones and quadratic potentials) protein structures from PDB (2JOF, 2WXC, 5AWL, 3GB1, 1UNC, 1PLW, 2MGO)
Benchmarks: synthetic loop folding (n=1000) protein folding energy and RMSD on six proteins
Metrics: final energy wall-clock time / speedup factor RMSD to PDB structure
Baselines: gradient descent with Adam OpenMM linear coarse-graining reparametrization
Builds on: coarse-graining Deep Image Prior Adam graph convolutional networks
Closest papers by meaning
- Gradual Optimization Learning for Conformational Energy Minimization (ICLR 2024 · similarity 0.89)
- Long-Short-Range Message-Passing: A Physics-Informed Framework to Capture Non-Local Interaction for Scalable Molecular Dynamics Simulation (ICLR 2024 · similarity 0.85)
- Exploit Your Latents: Coarse-Grained Protein Backmapping with Latent Diffusion Models (AAAI 2025 · similarity 0.84)
- Towards Fast, Specialized Machine Learning Force Fields: Distilling Foundation Models via Energy Hessians (ICLR 2025 · similarity 0.84)
- Pushing the Limits of All-Atom Geometric Graph Neural Networks: Pre-Training, Scaling, and Zero-Shot Transfer (ICLR 2025 · similarity 0.84)
- Amortized Molecular Optimization via Group Relative Policy Optimization (NeurIPS 2026 · similarity 0.84)
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