Align Your Structures: Generating Trajectories with Structure Pretraining for Molecular Dynamics
Organizations: Stanford University · Lambda, Inc
Abstract
Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.
Figures & tables
| Method | JSD (Mean — Median) ( ) | ||||||||||
| Bond Angle | Bond Length | Torsion | TICA_0 | TICA_0,1 | |||||||
| QM9 | MD Oracle | 0.042 | 0.028 | 0.032 | 0.031 | 0.192 | 0.134 | 0.318 | 0.291 | 0.413 | 0.394 |
| AR + EGNN | 0.702 | 0.677 | 0.770 | 0.780 | 0.702 | 0.761 | 0.770 | 0.788 | 0.820 | 0.824 | |
| AR + ET | 0.705 | 0.746 | 0.680 | 0.721 | 0.553 | 0.586 | 0.568 | 0.562 | 0.783 | 0.786 | |
| AR + GeoTDM | 0.752 | 0.746 | 0.699 | 0.694 | 0.466 | 0.506 | 0.456 | 0.463 | 0.714 | 0.719 | |
| GeoTDM | 0.691 | 0.690 | 0.676 | 0.670 | 0.489 | 0.527 | 0.449 | 0.453 | 0.691 | 0.694 | |
| Method | JSD (Mean — Median) (↓) | ||||||||
| Bond Angle | Bond Length | Torsion | TICA_0,1 | ||||||
| Mean | Median | Mean | Median | Mean | Median | Mean | Median | ||
| QM9 | EGInterpolator-N | 0.538 | 0.538 | 0.583 | 0.580 | 0.441 | 0.494 | 0.680 | 0.685 |
| EGInterpolator | 0.305 | 0.292 | 0.210 | 0.188 | 0.363 | 0.380 | 0.636 | 0.642 | |
| Drugs | EGInterpolator-S | 0.325 | 0.330 | 0.330 | 0.321 | 0.414 | 0.419 | 0.673 | 0.672 |
| EGInterpolator-N | 0.332 | 0.332 | 0.386 | 0.383 | 0.455 | 0.466 | 0.698 | 0.703 | |
Appendix figures & tables26 assets
Supplementary material from the paper’s appendix.
Appendix
| Metrics (JSD) | EGInterpolator | MDGen |
| Bond Angle (↓) | 0.092 | N/A |
| Bond Length (↓) | 0.056 | N/A |
| Torsion BB (↓) | 0.378 | 0.130 |
| Torsion SC (↓) | 0.189 | 0.093 |
| Torsion All (↓) | 0.265 | 0.109 |
| TICA 0 (↓) | 0.409 | 0.230 |
| Checkpoint | COV-R (%) | MAT-R (Å) | COV-P (%) | MAT-P (Å) | ||||
| Mean | Med. | Mean | Med. | Mean | Med. | Mean | Med. | |
| 99 | 90.18 | 94.59 | 0.2969 | 0.3049 | 55.23 | 51.36 | 0.4932 | 0.4823 |
| 539 | 87.62 | 92.03 | 0.2574 | 0.2613 | 58.12 | 53.24 | 0.4451 | 0.4445 |
| Method | Bond Angle | Bond Length | Torsion | TICA 0 | TICA 0,1 |
| GeoTDM | 0.640 0.645 | 0.643 0.645 | 0.498 0.503 | 0.531 0.550 | 0.712 0.720 |
| EGInterpolator-Simple | 0.208 0.192 | 0.258 0.244 | 0.385 0.399 | 0.462 0.465 | 0.660 0.662 |
| EGInterpolator-Casc | 0.173 0.153 | 0.142 0.112 | 0.377 0.388 | 0.454 0.441 | 0.650 0.644 |
| EGInterpolator-Casc-U | 0.220 0.202 | 0.195 0.168 | 0.414 0.429 | 0.499 0.496 | 0.689 0.697 |
| Method | JSD (Mean — Median) ( ) | ||||||||||
| Bond Angle | Bond Length | Torsion | TICA 0 | TICA 0,1 | |||||||
| QM9 | MD Oracle | 0.042 | 0.028 | 0.032 | 0.031 | 0.192 | 0.134 | 0.318 | 0.291 | 0.413 | 0.394 |
| GeoTDM | 0.691 | 0.690 | 0.676 | 0.670 | 0.489 | 0.527 | 0.449 | 0.453 | 0.691 | 0.694 | |
| EGInterpolator | 0.305 | 0.292 | 0.210 | 0.188 | 0.363 | 0.380 | 0.417 | 0.406 | 0.636 | 0.642 | |
| EGInterpolator-Both | 0.231 | 0.219 | 0.168 | 0.158 | 0.348 | 0.367 | 0.393 | 0.390 | 0.623 | 0.631 | |
| Drugs | MD Oracle | 0.036 | 0.023 | 0.030 | 0.028 | 0.215 | 0.131 | 0.484 | 0.494 | 0.610 | 0.630 |
| Dataset | EGInterpolator vs GT W1 | GeoTDM vs GT W1 |
| QM9 | 0.8127 | 2.9201 |
| Drugs | 0.7728 | 12.7664 |
| Metric | EGInterpolator vs GT W1 |
| Overall Energy W1 | 0.3806 |
| GeoTDM Energy W1 | 12.8636 |
| Block | Frame Range | Mean W1 |
| 1 | 1–250 | 0.2303 |
| 2 | 251–500 | 0.2778 |
| 3 | 501–750 | 0.3693 |
| 4 | 751–1000 | 0.2769 |
| 5 | 1001–1250 | 0.4541 |
| 6 | 1251–1500 | 0.3962 |
| Train Test | Method | Bond Angle | Bond Length | Torsion | TICA_0 | TICA_0,1 | |||||
| Mean | Med. | Mean | Med. | Mean | Med. | Mean | Med. | Mean | Med. | ||
| Standard Enlarged | GeoTDM | 0.690 | 0.690 | 0.674 | 0.668 | 0.488 | 0.529 | 0.452 | 0.451 | 0.695 | 0.699 |
| EGInterpolator-N | 0.539 | 0.538 | 0.584 | 0.582 | 0.447 | 0.492 | 0.438 | 0.440 | 0.678 | 0.685 | |
| EGInterpolator | 0.307 | 0.293 | 0.214 | 0.194 | 0.361 | 0.385 | 0.416 | 0.409 | 0.633 | 0.639 | |
| Enlarged Standard | GeoTDM | 0.757 | 0.757 | 0.782 | 0.793 | 0.488 | 0.533 | 0.454 | 0.453 | 0.697 | 0.703 |
| EGInterpolator-N | 0.470 | 0.460 | 0.540 | 0.544 | 0.433 | 0.481 | 0.443 | 0.440 | 0.681 | 0.691 | |
| Model | Bond Angle (↓) | Bond Length (↓) | Torsion (↓) |
| EGInterpolator Normal (QM9) | 0.305 / 0.292 | 0.210 / 0.188 | 0.363 / 0.380 |
| EGInterpolator (QM9) | 0.398 / 0.391 | 0.618 / 0.613 | 0.358 / 0.372 |
| EGInterpolator Normal (DRUGS) | 0.173 / 0.153 | 0.142 / 0.112 | 0.377 / 0.388 |
| EGInterpolator (DRUGS) | 0.435 / 0.445 | 0.580 / 0.091 | 0.378 / 0.382 |
| Dataset | GT MD | Original Gen. | Gen. | Shuffled GT | Shuffled Gen. |
| QM9 Test | 101.0 | 13.59 | 5.2 | 5.2 | 5.2 |
| Drugs Test | 130.1 | 185.64 | 5.2 | 5.2 | 5.2 |
| COV-R (%) | MAT-R (Å) | COV-P (%) | MAT-P (Å) | |||||
| Mean | Med. | Mean | Med. | Mean | Med. | Mean | Med. | |
| Casc | ||||||||
| 0.000 | 87.99 | 91.98 | 0.2539 | 0.2600 | 58.30 | 53.62 | 0.4430 | 0.4397 |
| 0.025 | 87.82 | 92.98 | 0.2570 | 0.2598 | 57.70 | 53.17 | 0.4470 | 0.4396 |
| 0.050 | 88.34 | 92.84 | 0.2568 | 0.2556 | 58.29 | 53.78 | 0.4460 | 0.4439 |
| 0.075 | 88.16 | 93.61 | 0.2577 | 0.2610 | 57.38 | 52.86 | 0.4490 | 0.4467 |
| Embedding Type | Input | Dimension |
| Atom Embedding | Atomic Number | 30 |
| Bond Embedding | No Bond, Bond Type, 2nd/3rd-order edge | 4 |
| Atom Features | |||
| Indices | Description | Options | Type |
| 0–1 | Aromaticity | true, false | One-hot |
| 2–7 | Hybridization | , , , , , other | One-hot |
| 8 | Partial charge | Value | |
| 9–16 | Implicit valence | 0, 1, 2, 3, 4, 5, 6, other | One-hot |
| 17–24 | Degree | 0, 1, 2, 3, 4, 5, 6, other | One-hot |
| Dataset & Duration | OpenMM MD | 4x Block Diffusion | Full Diffusion |
| Drugs (5.2 ns) | 584.52 | 201.70 | 161.08 |
| QM9 (2.6 ns) | 151.38 | - | 60.08 |
| SMILES | GT | EGInterpolator | GeoTDM |
| CC(CO)(CO)CC#N | |||
| COC[C@@]1(CO)N[C@H]1C | |||
| C#CCCC@HOCC | |||
| CCOCCCN1CC1 | |||
| CC(=O)C@HCCO | |||
| CCCC@@(CC)OC |
Molecular Dynamics Simulation
Molecular dynamics simulation models atomic motion to study molecular structure, material behavior, reactions, and thermodynamic properties.
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