Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Sahrmann, Patrick G.; Loose, Timothy D.; Durumeric, Aleksander E. P.; Voth, Gregory A.

doi:10.1021/acs.jctc.2c01183

Cited by 16 publications

(14 citation statements)

References 91 publications

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“…206 Voth and co-workers have also employed virtual sites to describe the local solvation environment in implicit solvent models of lipid bilayers. 207,272 Along similar lines, Lafond and Izvekov developed a bottom-up framework for modeling electrostatic interactions with virtual sites that describe effective polarizabilities. 273,274 Moreover, the intriguing Upside protein model describes protein side chains with virtual sites that interact via a complex many-body function of the backbone coordinates.…”

Section: Structural Fidelitymentioning

confidence: 99%

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

Noid

2023

J. Phys. Chem. B

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By averaging over atomic details, coarse-grained (CG) models provide profound computational and conceptual advantages for studying soft materials. In particular, bottom-up approaches develop CG models based upon information obtained from atomically detailed models. At least in principle, a bottom-up model can reproduce all the properties of an atomically detailed model that are observable at the resolution of the CG model. Historically, bottom-up approaches have accurately modeled the structure of liquids, polymers, and other amorphous soft materials, but have provided lower structural fidelity for more complex biomolecular systems. Moreover, they have also been plagued by unpredictable transferability and a poor description of thermodynamic properties. Fortunately, recent studies have reported dramatic advances in addressing these prior limitations. This Perspective reviews this remarkable progress, while focusing on its foundation in the basic theory of coarse-graining. In particular, we describe recent insights and advances for treating the CG mapping, for modeling many-body interactions, for addressing the state-point dependence of effective potentials, and even for reproducing atomic observables that are beyond the resolution of the CG model. We also outline outstanding challenges and promising directions in the field. We anticipate that the synthesis of rigorous theory and modern computational tools will result in practical bottom-up methods that not only are accurate and transferable but also provide predictive insight for complex systems.

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Section: Structural Fidelitymentioning

confidence: 99%

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

Noid

2023

J. Phys. Chem. B

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“…To describe the entropy of the system containing , using eq 9, we may first define the marginal probabilities using the matrix elements (17) and (18) to redefine eq 7 and eq 8 as (19) These marginals may be used to write the Shannon entropy functions:…”

Section: Description Of Entropymentioning

confidence: 99%

“…Of particular interest and with a great success is the use of the Restricted-Boltzmann Machine (RBM) . The choice of RBM is due to the fact it has been proven to be a universal approximator for any probability density − and has received astonishing success in simulating a wide variety of drivers in condensed-matter physics, , quantum dynamics vibration spectroscopy of molecular systems, , quantum chemistry − of complex multiscale problems, and even in standard classification tasks. , Prior work has also established that RBM is capable of mimicking a volume-law entangled quantum state even when sparsely parametrized . With quadratically scaling quantum circuits available, RBM also shows hints of possible quantum advantage due to proven intractability of polynomially retrieving the full distribution classically .…”

Section: Introductionmentioning

confidence: 99%

Analogy between Boltzmann Machines and Feynman Path Integrals

Iyengar

Kais

2023

J. Chem. Theory Comput.

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Machine learning has had a significant impact on multiple areas of science, technology, health, and computer and information sciences. Through the advent of quantum computing, quantum machine learning has developed as a new and important avenue for the study of complex learning problems. Yet there is substantial debate and uncertainty in regard to the foundations of machine learning. Here, we provide a detailed exposition of the mathematical connections between a general machine learning approach called Boltzmann machines and Feynman's description of quantum and statistical mechanics. In Feynman's description, quantum phenomena arise from an elegant, weighted sum over (or superposition of) paths. Our analysis shows that Boltzmann machines and neural networks have a similar mathematical structure. This allows the interpretation that the hidden layers in Boltzmann machines and neural networks are discrete versions of path elements and allows a path integral interpretation of machine learning similar to that in quantum and statistical mechanics. Since Feynman paths are a natural and elegant depiction of interference phenomena and the superposition principle germane to quantum mechanics, this analysis allows us to interpret the goal in machine learning as finding an appropriate combination of paths, and accumulated path-weights, through a network, that cumulatively captures the correct properties of an x-to-y map for a given mathematical problem. We are forced to conclude that neural networks are naturally related to Feynman path-integrals and hence may present one avenue to be considered as quantum problems. Consequently, we provide general quantum circuit models applicable to both Boltzmann machines and Feynman path integrals.

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“…8,9,22 For example, work has extensively studied the influence of the atom-to-bead mapping, 13,30,[37][38][39][40][41][42][43][44][45][46] functional form of candidate potential, 11,12,14,15,[47][48][49][50][51] and other details of the fitting routine. 19,32,33,[52][53][54][55][56] However, to our knowledge no work has directly and systematically investigated the influence of the mapping that projects fine-grained (FG) forces to the CG resolution. When considering the theoretical optimization statement defining force matching in the infinite-sample limit, this force mapping only affects a seemingly inconsequential constant offset to the variational statement determining the optimal force-field.…”

Section: Introductionmentioning

confidence: 99%

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Krämer¹,

Durumeric²,

Charron³

et al. 2023

Preprint

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Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning CG force-fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force-field on average. We show that there is flexibility in how to map all-atom forces to the CG representation, and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force-fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins Chignolin and Tryptophan Cage and published as open-source code.

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Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Cited by 16 publications

References 91 publications

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

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

Analogy between Boltzmann Machines and Feynman Path Integrals

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

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