Special Issue: Big data and predictive computational modeling

Koutsourelakis, Phaedon‐Stelios; Zabaras, Nicholas; Girolami, Mark

doi:10.1016/j.jcp.2016.03.028

Cited by 16 publications

(12 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…i) . The labels specify the utilized activation functions in the following manner: a (1) -a (2) -a (3) -ã (1) -ã (2) -ã (3) . We use…”

Section: Model Specificationmentioning

confidence: 99%

“…Molecular dynamics (MD) simulations, in combination with prevalent algorithmic enhancements and tremendous progress in computational resources, have contributed to new insights into mechanisms and processes present in physics, chemistry, biology and engineering. However, their applicability in systems of practical relevance poses insurmountable computational difficulties 1,2 . For example, the simulation of M = 10 5 atoms over a time horizon of a mere T ≈ 10 −4 s with a time step of ∆t = 10 −15 s implies a computational time of one year 3 .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Predictive collective variable discovery with deep Bayesian models

Schöberl

Zabaras

Koutsourelakis

2019

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the configurational space by enhanced sampling methods depends on the choice of collective variables (CVs). In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory. The ability to generate samples of the fine-scale atomistic configurations using limited training data allows us to compute estimates of observables as well as our probabilistic confidence on them. The methodology is based on emerging methodological advances in machine learning and variational inference. The discovered CVs are related to physicochemical properties which are essential for understanding mechanisms especially in unexplored complex systems. We provide a quantitative assessment of the CVs in terms of their predictive ability for alanine dipeptide (ALA-2) and ALA-15 peptide.

show abstract

“…i) . The labels specify the utilized activation functions in the following manner: a (1) -a (2) -a (3) -ã (1) -ã (2) -ã (3) . We use…”

Section: Model Specificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predictive collective variable discovery with deep Bayesian models

Schöberl

Zabaras

Koutsourelakis

2019

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…We adopt a data-based perspective [2,3] that relies on data generated by simulations of a fine-grained (FG) system in order to learn a coarse-grained (CG) model. We nevertheless note that such coarse-graining tasks exhibit fundamental differences from large-scale machine learn-ing tasks [4,5] as the data involved is usually small due to the expensive data acquisition and as information about the underlying physical structure of the problem is available. When this domain knowledge is incorporated into the CG model it can improve its predictive ability [6,7].…”

Section: Introductionmentioning

confidence: 99%

Physics-Aware, Deep Probabilistic Modeling of Multiscale Dynamics in the Small Data Regime

Kaltenbach¹,

Koutsourelakis²

2021

14th WCCM-ECCOMAS Congress

View full text Add to dashboard Cite

The data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a probabilistic perspective that simultaneously identifies predictive, lower-dimensional coarse-grained (CG) variables as well as their dynamics. We make use of the expressive ability of deep neural networks in order to represent the right-hand side of the CG evolution law. Furthermore, we demonstrate how domain knowledge that is very often available in the form of physical constraints (e.g. conservation laws) can be incorporated with the novel concept of virtual observables. Such constraints, apart from leading to physically realistic predictions, can significantly reduce the requisite amount of training data which enables reducing the amount of required, computationally expensive multiscale simulations (Small Data regime). The proposed state-space model is trained using probabilistic inference tools and, in contrast to several other techniques, does not require the prescription of a fine-to-coarse (restriction) projection nor time-derivatives of the state variables. The formulation adopted is capable of quantifying the predictive uncertainty as well as of reconstructing the evolution of the full, fine-scale system which allows to select the quantities of interest a posteriori. We demonstrate the efficacy of the proposed framework in a high-dimensional system of moving particles.

show abstract

“…For example, Napoletani et al (2014) identify new methodological ‘motifs’ emerging in the use of statistics and mathematics in biology. A panel at the Society for Industrial and Applied Mathematics’ 2015 Conference on Computational Science and Engineering addressed the topic ( Sterk & Johnson, 2015 ), as did a symposium on data and computer modelling also held in Spring 2015 ( Koutsourelakis et al, 2015 ). Also, see Donoho (2015) for a historically based view of how the big data movement relates to statistics and machine learning.…”

Section: Introductionmentioning

confidence: 99%

Will big data yield new mathematics? An evolving synergy with neuroscience

Feng

Holmes

2016

IMA J Appl Math

View full text Add to dashboard Cite

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

show abstract

Special Issue: Big data and predictive computational modeling

Cited by 16 publications

References 11 publications

Predictive collective variable discovery with deep Bayesian models

Predictive collective variable discovery with deep Bayesian models

Physics-Aware, Deep Probabilistic Modeling of Multiscale Dynamics in the Small Data Regime

Will big data yield new mathematics? An evolving synergy with neuroscience

Contact Info

Product

Resources

About