A Recursive Body-Body Formulation for Reducing the Computational Cost of Pairwise Coulomb Force Computation for Modeling and Simulation of Biopolymers, Using a Multibody Approach to Model Reduction

2013 ◽  
Author(s):  
Jeremy Laflin ◽  
Kurt Anderson
Keyword(s):  
Model Reduction ◽  
Charge Distribution ◽  
Computational Cost ◽  
Coulomb Force ◽  
Rigid Bodies ◽  
Inertia Tensor ◽  
Numerical Example ◽  
Pairwise Force ◽  
Body Formulation ◽  
Dynamics Simulations

This work presents a method for recursively assembling tensor-like quantities that parameterize the charge distribution of rigid bodies, which result from model reduction of biopolymeric systems using an articulated multibody approach. This is done with the goal of reducing the computational cost associated with the pairwise force determination encountered in molecular dynamics simulations. To achieve a linear computational cost complexity of the force determination, with respect to the number of bodies in the system (N), a recursive assembly and disassembly (evaluation) sweep is proposed. This work proposes assembling these tensor quantities (pseudo-inertia tensors), which are associated with the body’s charge distribution, with a method that uses the standard parallel axis theorem to shift these tensors to a common point so they may be summed. This work presents a preliminary numerical example that examines the accuracy of the force and moment computation using a pseudo-inertia tensor resulting after one level of recursive assembly. The Coulomb force and associated moment on a target body due to the assembled body is computed. The test problem approximates a system that is highly negatively or positively charged. The orientation of the bodies that are assembled is varied, along with the distance between the assembly and the target body. The preliminary results presented herein suggest that this is a viable method of efficiently representing the charge distribution of an assembly. The numerical example presented determines the Coulomb force and the associated moment, as a function of distance and the pseudo-inertia tensor. However, the approximation can be used for any force that is of the form 1/rs, where s is any power.

Parameterization of Divalent Cations for Coarse-Grained Simulations

2020 ◽  
Author(s):  
Florencia Klein ◽  
Daniela Cáceres-Rojas ◽  
Monica Carrasco ◽  
Juan Carlos Tapia ◽  
Julio Caballero ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Metal Ions ◽  
Molecular Dynamics Simulations ◽  
Divalent Cations ◽  
Computational Cost ◽  
Data Bank ◽  
Coarse Grained ◽  
Interaction Parameters ◽  
Dynamics Simulations ◽  
Dynamical Description

<p>Although molecular dynamics simulations allow for the study of interactions among virtually all biomolecular entities, metal ions still pose significant challenges to achieve an accurate structural and dynamical description of many biological assemblies. This is particularly the case for coarse-grained (CG) models. Although the reduced computational cost of CG methods often makes them the technique of choice for the study of large biomolecular systems, the parameterization of metal ions is still very crude or simply not available for the vast majority of CG- force fields. Here, we show that incorporating statistical data retrieved from the Protein Data Bank (PDB) to set specific Lennard-Jones interactions can produce structurally accurate CG molecular dynamics simulations. Using this simple approach, we provide a set of interaction parameters for Calcium, Magnesium, and Zinc ions, which cover more than 80% of the metal-bound structures reported on the PDB. Simulations performed using the SIRAH force field on several proteins and DNA systems show that using the present approach it is possible to obtain non-bonded interaction parameters that obviate the use of topological constraints. </p>

Active Learning Accelerates Ab Initio Molecular Dynamics on Pericyclic Reactive Energy Surfaces

2020 ◽  
Author(s):  
Shi Jun Ang ◽  
Wujie Wang ◽  
Daniel Schwalbe-Koda ◽  
Simon Axelrod ◽  
Rafael Gomez-Bombarelli
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Transition State ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface ◽  
Computational Cost ◽  
Reactive Trajectories ◽  
Dynamics Simulations ◽  
Energy Surfaces

<div>Modeling dynamical effects in chemical reactions, such as post-transition state bifurcation, requires <i>ab initio</i> molecular dynamics simulations due to the breakdown of simpler static models like transition state theory. However, these simulations tend to be restricted to lower-accuracy electronic structure methods and scarce sampling because of their high computational cost. Here, we report the use of statistical learning to accelerate reactive molecular dynamics simulations by combining high-throughput ab initio calculations, graph-convolution interatomic potentials and active learning. This pipeline was demonstrated on an ambimodal trispericyclic reaction involving 8,8-dicyanoheptafulvene and 6,6-dimethylfulvene. With a dataset size of approximately</div><div>31,000 M062X/def2-SVP quantum mechanical calculations, the computational cost of exploring the reactive potential energy surface was reduced by an order of magnitude. Thousands of virtually costless picosecond-long reactive trajectories suggest that post-transition state bifurcation plays a minor role for the reaction in vacuum. Furthermore, a transfer-learning strategy effectively upgraded the potential energy surface to higher</div><div>levels of theory ((SMD-)M06-2X/def2-TZVPD in vacuum and three other solvents, as well as the more accurate DLPNO-DSD-PBEP86 D3BJ/def2-TZVPD) using about 10% additional calculations for each surface. Since the larger basis set and the dynamic correlation capture intramolecular non-covalent interactions more accurately, they uncover longer lifetimes for the charge-separated intermediate on the more accurate potential energy surfaces. The character of the intermediate switches from entropic to thermodynamic upon including implicit solvation effects, with lifetimes increasing with solvent polarity. Analysis of 2,000 reactive trajectories on the chloroform PES shows a qualitative agreement with the experimentally-reported periselectivity for this reaction. This overall approach is broadly applicable and opens a door to the study of dynamical effects in larger, previously-intractable reactive systems.</div>

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

2018 ◽  
Author(s):  
Benjamin R. Jagger ◽  
Christoper T. Lee ◽  
Rommie Amaro
Keyword(s):  
Molecular Dynamics ◽  
Drug Discovery ◽  
Small Molecule ◽  
Brownian Dynamics ◽  
Model Simulation ◽  
Computational Cost ◽  
Lead Selection ◽  
Delta G ◽  
Dynamics Simulations

<p>The ranking of small molecule binders by their kinetic (kon and koff) and thermodynamic (delta G) properties can be a valuable metric for lead selection and optimization in a drug discovery campaign, as these quantities are often indicators of in vivo efficacy. Efficient and accurate predictions of these quantities can aid the in drug discovery effort, acting as a screening step. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon’s, koff’s, and G’s. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, -cyclodextrin, based on predicted kon’s and koff’s. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long-timescale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish “best practices” for its future use.</p>

scholarly journals Prediction of Crosswind Separation Velocity for Fan and Nacelle Systems Using Body Force Models: Part 1: Fan Body Force Model Generation without Detailed Stage Geometry

2019 ◽  
Vol 4 (4) ◽  
pp. 43 ◽  
Author(s):  
Quentin J. Minaker ◽  
Jeffrey J. Defoe
Keyword(s):  
Design Process ◽  
Body Force ◽  
Pressure Ratio ◽  
Computational Cost ◽  
The Body ◽  
Force Model ◽  
Limited Access ◽  
Turbofan Engines ◽  
Simplifying Assumptions ◽  
Dynamics Simulations

Modern aircraft engines must accommodate inflow distortions entering the engines as a consequence of modifying the size, shape, and placement of the engines and/or nacelle to increase propulsive efficiency and reduce aircraft weight and drag. It is important to be able to predict the interactions between the external flow and the fan early in the design process. This is challenging due to computational cost and limited access to detailed fan/engine geometry. In this, the first part of a two part paper, we present a design process that produces a fan gas path and body force model with performance representative of modern high bypass ratio turbofan engines. The target users are those with limited experience in turbomachinery design or limited access to fan geometry. We employ quasi-1D analysis and a series of simplifying assumptions to produce a gas path and the body force model inputs. Using a body force model of the fan enables steady computational fluid dynamics simulations to capture fan–distortion interaction. The approach is verified for the NASA Stage 67 transonic fan. An example of the design process is also included; the model generated is shown to meet the desired fan stagnation pressure ratio and thrust to within 1%.

A Numerical Example of Alternator Model Reduction to Be Given in a Classroom

1988 ◽  
Vol 25 (4) ◽  
pp. 341-349
Author(s):  
Mohamed B. A. Kamoun ◽  
Michel Poloujadoff
Keyword(s):  
Transmission Line ◽  
Model Reduction ◽  
Stability Study ◽  
Computer Solution ◽  
Numerical Example

The authors give a numerical example of a stability study of an alternator connected to an infinite bus through a transmission line. Possible reductions of the model are carefully considered. This paper is intended to be the basis of exercises submitted to students for a computer solution.

An Energy Closure Criterion for Model Reduction of a Kicked Euler–Bernoulli Beam

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Suparno Bhattacharyya ◽  
Joseph P. Cusumano
Keyword(s):  
Model Reduction ◽  
Mode Selection ◽  
Computational Cost ◽  
Impulsive Loading ◽  
Bernoulli Beam ◽  
Full System ◽  
Fixed Amount ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Euler Bernoulli Beam

Abstract Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler–Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system’s response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system’s true behavior.

scholarly journals Complexity Reduction of Multiphase Flows in Heterogeneous Porous Media

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 144-151 ◽  
Author(s):  
Mehdi Ghommem ◽  
Eduardo Gildin ◽  
Mohammadreza Ghasemi
Keyword(s):  
Porous Media ◽  
Model Reduction ◽  
Flow Behavior ◽  
Computational Cost ◽  
Heterogeneous Porous Media ◽  
Production Optimization ◽  
Dynamic Mode ◽  
Two Phase ◽  
Fine Grid ◽  
Mode Decomposition

Summary In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in heterogeneous porous media. We propose intrusive and nonintrusive model-reduction approaches that enable a significant reduction in the size of the subsurface flow problem while capturing the behavior of the fully resolved solutions. In one approach, we use the dynamic mode decomposition. This approach does not require any modification of the reservoir simulation code but rather post-processes a set of global snapshots to identify the dynamically relevant structures associated with the flow behavior. In the second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper-orthogonal-decomposition modes. Furthermore, we use the discrete empirical interpolation method to approximate the mobility-related term in the global-system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE-10 benchmark permeability field, and present a numerical example in two-phase flow. One can efficiently use the proposed model-reduction methods in the context of uncertainty quantification and production optimization.

Development of a Multistage Reliability-Based Design Optimization Method

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Eric J. Paulson ◽  
Ryan P. Starkey
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Technology Development ◽  
Computational Cost ◽  
Optimization Method ◽  
Comparison Method ◽  
Reliability Based Design Optimization ◽  
Numerical Example ◽  
Reliability Based Design ◽  
System Acquisition

Complex system acquisition and its associated technology development have a troubled recent history. The modern acquisition timeline consists of conceptual, preliminary, and detailed design followed by system test and production. The evolving nature of the estimates of system performance, cost, and schedule during this extended process may be a significant contribution to recent issues. The recently proposed multistage reliability-based design optimization (MSRBDO) method promises improvements over reliability-based design optimization (RBDO) in achieved objective function value. In addition, its problem formulation more closely resembles the evolutionary nature of epistemic design uncertainties inherent in system design during early system acquisition. Our goal is to establish the modeling basis necessary for applying this new method to the engineering of early conceptual/preliminary design. We present corrections in the derivation and solutions to the single numerical example problem published by the original authors, Nam and Mavris, and examine the error introduced under the reduced-order reliability sampling used in the original publication. MSRBDO improvements over the RBDO solution of 10–36% for the objective function after first-stage optimization are shown for the original second-stage example problem. A larger 26–40% improvement over the RBDO solution is shown when an alternative comparison method is used than in the original. The specific implications of extending the method to arbitrary m-stage problems are presented, together with a solution for a three-stage numerical example. Several approaches are demonstrated to mitigate the computational cost increase of MSRBDO over RBDO, resulting in a net decrease in calculation time of 94% from an initial MSRBDO baseline algorithm.

scholarly journals Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

2021 ◽  
Author(s):  
Kazuumi Fujioka ◽  
Yuheng Luo ◽  
Rui Sun
Keyword(s):  
Machine Learning ◽  
Ab Initio ◽  
Density Functional ◽  
Computational Cost ◽  
Basis Sets ◽  
Intrinsic Reaction Coordinate ◽  
Chemical Systems ◽  
Energy Gradient ◽  
Gradient Calculation ◽  
Dynamics Simulations

Ab initio molecular dymamics (AIMD) simulation studies are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of the ab initio energy gradient calculations needed for AIMD, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been employed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called interpolating moving ridge regression (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and the predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. The method is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

scholarly journals Simulating Protein-Ligand Binding with Neural Network Potentials

2019 ◽  
Author(s):  
Shae-Lynn Lahey ◽  
Christopher Rowley
Keyword(s):  
Neural Network ◽  
Ligand Binding ◽  
Computational Cost ◽  
Bound State ◽  
Drug Binding ◽  
Cancer Drug ◽  
Molecular Conformations ◽  
Drug Molecules ◽  
The Stability ◽  
Dynamics Simulations

Drug molecules adopt a range of conformations both in solution and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermolecular interactions that drive protein–ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of molecular conformations with accuracy comparable to state-of-the-art quantum chemical calculations but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramolecular forces of protein-bound drugs within molecular dynamics simulations. These simulations are shown to be capable of predicting the protein–ligand binding pose and conformational component of the absolute Gibbs energy of binding for a set of drug molecules. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to considerably overestimated by a molecular mechanical model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic molecules, reasonable binding poses are predicted for charged ligands, although this method is not suitable for modeling the ligands in solution.

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