CGSchNet Model: Coarse-Grained MD

• CGSchNet is a neural network model that uses graph representations to generate coarse-grained force fields capturing essential protein thermodynamics and kinetics.
• It employs force and energy matching techniques to reconcile atomistic simulation data with efficient coarse-grained representations.
• The model integrates active learning and enhanced sampling, enabling targeted data augmentation and robust benchmarking of protein dynamics.

The CGSchNet model is a neural network architecture developed for coarse-grained molecular dynamics simulations, specifically designed to generate physically accurate force fields that capture the essential thermodynamic and kinetic properties of biomolecular systems. CGSchNet uses a graph neural network representation to predict forces and energetics on coarse-grained beads, such as the $C_\alpha$ atoms in proteins, enabling efficient exploration of protein conformational spaces. It has been widely used in recent research for tasks including free energy surface matching, active learning, and standardized benchmarking in protein molecular dynamics.

1. Architecture and Methodology

CGSchNet is built around a graph neural network (GNN) that takes coarse-grained molecular coordinates as input, representing individual beads and their interconnections using edge features (primarily distances and potentially angles). The network predicts the effective potential energy $U_\theta(\mathbf{R})$ for the configuration $\mathbf{R}$ and computes forces as $-\nabla_{\mathbf{R}} U_\theta(\mathbf{R})$. Central operations include the mapping of all-atom (AA) configurations $\mathbf{r}$ into coarse-grained (CG) representations $\mathbf{R}$ using a linear projection operator: $\mathbf{R} = \Xi \mathbf{r}$ Forces in CG space are similarly projected: $$\mathbf{F}_{\mathrm{CG}} = \Xi_F \mathbf{f}_{AA}, \qquad \Xi_F = (\Xi \Xi^\top)^{-1} \Xi$$ The model is typically trained by minimizing a force matching loss: $$\mathcal{L}_{FM}(\theta) = \frac{1}{T}\sum_{t=1}^{T} \frac{1}{3M^{(t)}} \|\mathbf{F}_\theta(\mathbf{R}^{(t)}) - \mathbf{F}_{\mathrm{CG}}^{(t)}\|_F^2$$ Training data is generated from atomistic simulations, and the force field is fitted to reproduce the gradient structure of the underlying high-dimensional potential.

2. Force Matching and Energy Matching

Traditional coarse-grained modeling relies primarily on force matching, which aligns the predicted forces of the model to those of atomistic simulations. This is sufficient for reproducing local dynamics but can fail to accurately encode the overall thermodynamic landscape, particularly the relative depths of free energy wells in complex proteins (Aghili et al., 18 Sep 2025).

To address this, CGSchNet has incorporated an additional energy matching term into the loss function: $$L(\theta) = \lambda_{\mathrm{force}} L_{\mathrm{force}}(\theta) + \lambda_{\mathrm{energy}} L_{\mathrm{energy}}(\theta)$$ where

$$L_{\mathrm{energy}}(\theta) = \frac{1}{N} \sum_{i=1}^N [ U(\theta, R_i) - G(R_i) + C ]$$

$U(\theta, R_i)$ is the predicted energy, $G(R_i)$ is the reference free energy obtained via Boltzmann inversion from TICA-projected probability densities, and $C$ is a protein-specific additive constant. The constraint $$\lambda_{\mathrm{force}} + \lambda_{\mathrm{energy}} = 1$$ governs the trade-off.

Empirical findings reveal that low $\lambda_{\mathrm{energy}}$ preserves generalization and physical barriers, while high values induce overfitting to deep minima, suppressing transition barriers and distorting energy landscapes. This suggests that precise tuning of $\lambda_{\mathrm{energy}}$ is crucial for balancing local accuracy and global thermodynamic fidelity.

3. Active Learning Integration

The active learning framework implemented with CGSchNet allows for efficient exploration and correction of the model in poorly sampled regions (Bachelor et al., 21 Sep 2025). The procedure is as follows:

1. The CGSchNet model is initially trained on available data.
2. A CG simulation is run to generate new configurations.
3. For each new configuration, the RMSD to the training set is evaluated.
4. High-RMSD frames are flagged as under-sampled conformations.
5. These frames are backmapped to AA space and simulated briefly using an oracle (e.g., OpenMM).
6. The new AA simulation data is projected back to CG features.
7. The CGSchNet model is retrained on the augmented set.

This cyclic procedure targets data augmentation where it is most needed, correcting the force field at coverage gaps while preserving the efficiency of CG-level simulations. Quantitatively, the framework has demonstrated a 33.05% improvement in the Wasserstein-1 (W1) metric in TICA space for Chignolin, indicating more accurate agreement with the ground truth distribution.

4. Benchmarking and Enhanced Sampling

In standardized benchmarking, CGSchNet is deployed within a modular framework based on weighted ensemble (WE) sampling using the WESTPA toolkit (Aghili et al., 20 Oct 2025). The CGSchNet propagator is integrated as a simulation engine that generates coarse-grained MD trajectories. WESTPA’s resampling scheme adaptively boosts sampling in rare transition regions and assigns statistical weights to trajectories for unbiased property reconstruction.

The framework utilizes TICA-derived progress coordinates for dimensionality reduction and enhanced sampling. Model variants are benchmarked as follows:

• Fully trained CGSchNet: trained on all MD frames.
• Under-trained CGSchNet: trained on only a fraction of frames (e.g., 10%).

Metrics computed include kernel density overlap in TICA space, Wasserstein-1 ($W_1$) distance, Kullback-Leibler (KL) divergence, contact map differences, and local observables like bond lengths, angles, dihedrals, and radius of gyration: $$R_g = \sqrt{\frac{1}{N} \sum_{i=1}^N \| \mathbf{r}_i - \mathbf{r}_{\mathrm{com}} \|^2}$$ A fully trained model shows close overlap with all-atom ground truth, whereas under-trained models exhibit instability and poor coverage, such as implosions or explosions in protein folding trajectories. This supports the view that training completeness is essential for physically meaningful ML-driven simulations.

5. Practical Applications and Limitations

CGSchNet accelerates MD simulations by orders of magnitude compared to AA force fields, enabling the exploration of large conformational spaces. Performance metrics show substantial improvement over naive force-matched networks when active learning and energy matching are adequately employed. The methodology supports:

• Efficient exploration of folding landscapes for small to medium proteins.
• Quantitative assessment with more than 19 geometrical and thermodynamic metrics.
• Correction of CG potentials in high-uncertainty regions identified by RMSD.

Limitations arise primarily in energy landscape generalization: excessive weighting of the energy loss leads to distortion of the landscape, and insufficient training data causes nonphysical sampling. The method’s efficacy diminishes for highly complex proteins where sampling deep minima and high barriers require more robust energy estimation techniques, such as integrating Markov State Models.

6. Future Directions

Multiple avenues have been identified for further advancement of CGSchNet-based frameworks:

• Improved energy surface estimation, leveraging MSM-derived stationary distributions or enhanced density estimation in TICA space.
• Development of multi-modal or adaptive loss functions to balance local force accuracy and global energy landscape fidelity.
• Extension to more complex proteins, expanding benchmarks to cover broad topologies and folding challenges.
• Synthesis of benchmark datasets with known features for controlled evaluation of force landscape accuracy and basin recovery.

A plausible implication is the emergence of hybrid ML–physics frameworks that incorporate both kinetic and thermodynamic constraints, guided by active learning and WE sampling, for next-generation protein simulation.

7. Summary Table: CGSchNet Capabilities in Recent Literature

Research Domain	Key Functionality	Performance/Data Insights
Free energy surface matching (Aghili et al., 18 Sep 2025)	Force and energy matching, TICA analysis	Overfitting at high energy loss weight; aligned surfaces at low energy weight
Active learning correction (Bachelor et al., 21 Sep 2025)	RMSD-based frame selection; on-the-fly AA simulation	33.05% improvement in W1 metric for Chignolin
Standardized benchmarking (Aghili et al., 20 Oct 2025)	Integration with WE sampling, quantitative metrics	Fully trained model matches ground truth; under-trained model unstable

CGSchNet represents a convergence of graph neural networks, enhanced sampling, and active learning for physically robust molecular dynamics in protein systems. Its validation in standardized frameworks and deployment in active learning loops establish it as a reference approach for coarse-grained MD validation, provided sufficient training and appropriate energy loss calibration are achieved.