Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA

Abstract

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss−Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood−Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarsegrained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

Perspective: Advances, Challenges, and Insight for Predictive Coarse-Grained Models

“…142 Recent studies indicate that integral equation methods can improve the efficiency and convergence properties of IBI and IMC. 146,148 While ML methods have proven useful for parametrizing topdown models to reproduce thermodynamic properties, 149−153 they have also recently been harnessed to parametrize physicsbased potentials in a bottom-up fashion. For instance, Hajizadeh and co-workers employed a genetic algorithm to parametrize top-down nonbonded potentials that matched temperaturedependent density measurements, while employing an artificial neural network (ANN) to parametrize bottom-up bonded potentials based upon information from united atom polymer simulations.…”

“…Both IBI and IMC systematically refine each interaction potential, U ζ ( x ), until simulations with the CG model reproduce the mapped probability distribution, p ζ ( x ), for the corresponding degree of freedom, ψ ζ , i.e., P ζ ( x ; U ) = p ζ ( x ) . While IMC explicitly treats the correlations between interactions when updating these potentials, IBI does not account for these correlations, which can lead to practical difficulties in converging the myriad potentials that are necessary for modeling complex systems with many distinct site types. − Because the resulting pair potentials tend to dramatically overestimate the internal pressure, they are often modified with a linear pressure correction that can be tuned to match the AA internal pressure while minimally impacting the structural fidelity of the CG model . Recent studies indicate that integral equation methods can improve the efficiency and convergence properties of IBI and IMC. , …”

“…In so doing, these benchmarking studies will make the “zoo” of bottom-up approaches both more comprehensible and also more accessible to the simulation community. One important step in this direction is the further development of new and existing ,,− open source software for bottom-up methods that is not only rigorous and robust but also well documented and easily used by other groups. As in much of computational chemistry, the community will greatly benefit from the development and distribution of automated work-flows for applying bottom-up methods.…”

Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation

“…Effective potentials derived from structure-based coarse-graining often show (thermodynamic) state dependence, e.g., temperature, , composition, etc., even after the optimization. Additional constraints can be introduced to the coarse-graining process to improve the transferability and representability of the structure-based CG model. − In structural coarse-graining, we believe that achieving an accurate CG model can be transformed into a problem of efficient multiobjective optimization with constraints.…”

Synthetic Force-Field Database for Training Machine Learning Models to Predict Mobility-Preserving Coarse-Grained Molecular-Simulation Potentials

“…After completion of the 608 AA MD runs, we employed the IBI , method to generate corresponding CG models using the VOTCA software package. − Each molecule was represented as a single bead mapped to the center of mass of the AA molecule. The AA trajectories were mapped over the whole production run of 10 ns, and we calculated the pair-correlation function between these beads.…”