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Register a new userMachine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems
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Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab-initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multi-body terms that emerge from the dimensionality reduction.
We assess Gaussian process (GP) regression as a technique to model interatomic forces in metal nanoclusters by analysing the performance of 2-body, 3-body and many-body kernel functions on a set of 19-atom Ni cluster structures. We find that 2-body GP kernels fail to provide faithful force estimates, despite succeeding in bulk Ni systems. However, both 3- and many-body kernels predict forces within a $sim$0.1 eV/$text{AA}$ average error even for small training datasets, and achieve high accuracy even on out-of-sample, high temperature, structures. While training and testing on the same structure always provides satisfactory accuracy, cross-testing on dissimilar structures leads to higher prediction errors, posing an extrapolation problem. This can be cured using heterogeneous training on databases that contain more than one structure, which results in a good trade-off between versatility and overall accuracy. Starting from a 3-body kernel trained this way, we build an efficient non-parametric 3-body force field that allows accurate prediction of structural properties at finite temperatures, following a newly developed scheme [Glielmo et al. PRB 97, 184307 (2018)]. We use this to assess the thermal stability of Ni$_{19}$ nanoclusters at a fractional cost of full ab initio calculations.
Machine learning algorithms have recently emerged as a tool to generate force fields which display accuracies approaching the ones of the ab-initio calculations they are trained on, but are much faster to compute. The enhanced computational speed of machine learning force fields results key for modelling metallic nanoparticles, as their fluxionality and multi-funneled energy landscape needs to be sampled over long time scales. In this review, we first formally introduce the most commonly used machine learning algorithms for force field generation, briefly outlining their structure and properties. We then address the core issue of training database selection, reporting methodologies both already used and yet unused in literature. We finally report and discuss the recent literature regarding machine learning force fields to sample the energy landscape and study the catalytic activity of metallic nanoparticles.
The mechanical properties of DNA are typically described by elastic theories with purely local couplings (on-site models). We discuss and analyze coarse-grained (oxDNA) and all-atom simulations, which indicate that in DNA distal sites are coupled. Hence, off-site models provide a more realistic description of the mechanics of the double helix. We show that off-site interactions are responsible for a length scale dependence of the elasticity, and we develop an analytical framework to estimate bending and torsional persistence lengths in models including these interactions. Our simulations indicate that off-site couplings are particularly strong for certain degrees of freedom, while they are very weak for others. If stiffness parameters obtained from DNA data are used, the theory predicts large length scale dependent effects for torsional fluctuations and a modest effect in bending fluctuations, which is in agreement with experiments.
Using a coarse-grained model, self-organized assembly of proteins (e.g. CorA and its inner segment iCorA) is studied by examining quantities such as contact profile, radius of gyration, and structure factor as a function of protein concentration at a range of low (native phase) to high (denature phase) temperatures. Visual inspections show distinct structures, i.e. isolated globular bundles to entangled network on multiple length scales in dilute to crowded protein concentrations. In native phase, the radius of gyration of the protein does not vary much with the protein concentration while that of its inner segment increases systematically. In contrast, the radius of gyration of the protein shows enormous growth with the concentration due to entanglement while that of the inner segment remains almost constant in denatured phase. The multi-scale morphology of the collective assembly is quantified by estimating the effective dimension D of protein from scaling of the structure factor: collective assembly from inner segments remains globular (D aroud 3) at almost all length scales in its native phase while that from protein chains shows sparsely distributed morphology with D around 2 in entire temperature range due to entanglement except in crowded environment at low temperature where D around 2.6. Higher morphological response of chains with only the inner-segments due to selective interactions in its native phase may be more conducive to self-organizing mechanism than that of the remaining segments of the protein chains.
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