Density functional theory (DFT) has been applied to modeling molecular interactions in water for over three decades. The ubiquity of water in chemical and biological processes demands a unified understanding of its physics, from the single molecule to the thermodynamic limit and everything in between. Recent advances in the development of data-driven and machine-learning potentials have accelerated simulation of water and aqueous systems with DFT accuracy. However, anomalous properties of water in the condensed phase, where a rigorous treatment of both local and non-local many-body (MB) interactions is in order, are often unsatisfactory or partially missing in DFT models of water. In this review, we discuss the modeling of water and aqueous systems based on DFT and provide a comprehensive description of a general theoretical/computational framework for the development of data-driven many-body potentials from DFT reference data. This framework, coined MB-DFT, readily enables efficient many-body molecular dynamics (MD) simulations of small molecules, in both gas and condensed phases, while preserving the accuracy of the underlying DFT model. Theoretical considerations are emphasized, including the role that the delocalization error plays in MB-DFT potentials of water and the possibility to elevate DFT and MB-DFT to near-chemical-accuracy through a density-corrected formalism. The development of the MB-DFT framework is described in detail, along with its application in MB-MD simulations and recent extension to the modeling of reactive processes in solution within a quantum mechanics/MB molecular mechanics (QM/MB-MM) scheme, using water as a prototypical solvent. Finally, we identify open challenges and discuss future directions for MB-DFT and QM/MB-MM simulations in condensed phases.
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Multiscale Modeling Meets Machine Learning: What Can We Learn?
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse
and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. This review serves as introduction to a special issue on Uncertainty Quantification, Machine Learning, and Data-Driven Modeling of
Biological Systems that will help identify current roadblocks and areas where computational mechanics, as a discipline, can play a significant role. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.
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- NSF-PAR ID:
- 10157400
- Date Published:
- Journal Name:
- Archives of Computational Methods in Engineering
- ISSN:
- 1134-3060
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11831-020-09405-5
