Path Sampling Research Articles

Doppler Time-of-Flight Rendering

We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling. We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance.

Molecular Free Energies, Rates, and Mechanisms from Data-Efficient Path Sampling Simulations.

Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this limitation by collecting unbiased trajectories and capturing the relevant events. Moreover, the integration of machine learning can boost the sampling while simultaneously learning a quantitative representation of the mechanism. Still, the resulting trajectories are by construction non-Boltzmann-distributed, preventing the calculation of free energies and rates. We developed an algorithm to approximate the equilibrium path ensemble from machine-learning-guided path sampling data. At the same time, our algorithm provides efficient sampling, mechanism, free energy, and rates of rare molecular events at a very moderate computational cost. We tested the method on the folding of the mini-protein chignolin. Our algorithm is straightforward and data-efficient, opening the door to applications in many challenging molecular systems.

World‐Space Spatiotemporal Path Resampling for Path Tracing

AbstractWith the advent of hardware‐accelerated ray tracing, more and more real‐time rendering applications tend to render images with ray‐traced global illumination (GI). However, the low sample counts at real‐time framerates bring enormous challenges to existing path sampling methods. Recent work (ReSTIR GI) samples indirect illumination effectively with a dramatic bias reduction. However, as a screen‐space based path resampling approach, it can only reuse the path at the first bounce and brings subtle benefits for complex scenes. To this end, we propose a world‐space based spatiotemporal path resampling approach. Our approach caches more path samples into a world‐space grid, which allows reusing sub‐path starting from non‐primary path vertices. Furthermore, we introduce a practical normal‐aware hash grid construction approach, providing more efficient candidate samples for path resampling. Eventually, our method achieves improvements ranging from 16.6% to 41.9% in terms of mean squared errors (MSE) compared against the previous method with only 4.4% ∼ 8.4% extra time cost.

Efficient Caustics Rendering via Spatial and Temporal Path Reuse

AbstractCaustics are complex optical effects caused by the light being concentrated in a small area due to reflection or refraction on surfaces with low roughness, typically under a sharp light source. Rendering caustic effects is challenging for Monte Carlo‐based approaches, due to the difficulties of sampling the specular paths. One effective solution is using the specular manifold to locate these valid specular paths. Unfortunately, it needs many iterations to find these paths, leading to a long rendering time. To address this issue, our key insight is that the specular paths tend to be similar for neighboring shading points. To this end, we propose to reuse the specular paths spatially. More specifically, we generate some specular path samples with a low sample rate and then reuse these specular path samples as the initialization for specular manifold walk among neighboring shading points. In this way, much fewer specular path‐searching iterations are performed, due to the efficient initialization close to the final solution. Furthermore, this reuse strategy can be extended for dynamic scenes in a temporal manner, such as light moving or specular geometry deformation. Our method outperforms current state‐of‐the‐art methods and can handle multiple bounces of light and various scenes.

Elucidation of binding mechanism, affinity, and complex structure between mWT1 tumor-associated antigen peptide and HLA-A*24:02.

We have applied our advanced computational and experimental methodologies to investigate the complex structure and binding mechanism of a modified Wilms' Tumor 1 (mWT1) protein epitope to the understudied Asian-dominant allele HLA-A*24:02 (HLA-A24) in aqueous solution. We have applied our developed multicanonical molecular dynamics (McMD)-based dynamic docking method to analyze the binding pathway and mechanism, which we verified by comparing the highest probability structures from simulation with our experimentally solved x-ray crystal structure. Subsequent path sampling MD simulations elucidated the atomic details of the binding process and indicated that first an encounter complex is formed between the N-terminal's positive charge of the 9-residue mWT1 fragment peptide and a cluster of negative residues on the surface of HLA-A24, with the major histocompatibility complex (MHC) molecule preferring a predominantly closed conformation. The peptide first binds to this closed MHC conformation, forming an encounter complex, after which the binding site opens due to increased entropy of the binding site, allowing the peptide to bind to form the native complex structure. Further sequence and structure analyses also suggest that although the peptide loading complex would help with stabilizing the MHC molecule, the binding depends in a large part on the intrinsic affinity between the MHC molecule and the antigen peptide. Finally, our computational tools and analyses can be of great benefit to study the binding mechanism of different MHC types to their antigens, where it could also be useful in the development of higher affinity variant peptides and for personalized medicine.

Global analysis of energy landscapes for materials modeling: A test case for C60.

In this contribution, we employ computational tools from the energy landscape approach to test Gaussian Approximation Potentials (GAPs) for C60. In particular, we apply basin-hopping global optimization and explore the landscape starting from the low-lying minima using discrete path sampling. We exploit existing databases of minima and transition states harvested from previous work using tight-binding potentials. We explore the energy landscape for the full range of structures and pathways spanning from the buckminsterfullerene global minimum up to buckybowls. In the initial GAP model, the fullerene part of the landscape is reproduced quite well. However, there are extensive families of C1@C59 and C2@C58 structures that lie lower in energy. We succeeded in refining the potential to remove these artifacts by simply including two minima from the C2@C58 families found by global landscape exploration. We suggest that the energy landscape approach could be used systematically to test and improve machine learning interatomic potentials.

Conditioning Boltzmann generators for rare event sampling

Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of transition paths using a random walk in trajectory space. This, however, comes with the drawback of strong correlations between subsequently sampled paths and with an intrinsic difficulty in parallelizing the sampling process. We propose a transition path sampling scheme based on neural-network generated configurations. These are obtained employing normalizing flows, a neural network class able to generate statistically independent samples from a given distribution. With this approach, not only are correlations between visited paths removed, but the sampling process becomes easily parallelizable. Moreover, by conditioning the normalizing flow, the sampling of configurations can be steered towards regions of interest. We show that this approach enables the resolution of both the thermodynamics and kinetics of the transition region for systems that can be sampled using exact-likelihood generative models.

Worth the Weight: Sub-Pocket EXplorer (SubPEx), a Weighted Ensemble Method to Enhance Binding-Pocket Conformational Sampling.

Structure-based virtual screening (VS) is an effective method for identifying potential small-molecule ligands, but traditional VS approaches consider only a single binding-pocket conformation. Consequently, they struggle to identify ligands that bind to alternate conformations. Ensemble docking helps address this issue by incorporating multiple conformations into the docking process, but it depends on methods that can thoroughly explore pocket flexibility. We here introduce Sub-Pocket EXplorer (SubPEx), an approach that uses weighted ensemble (WE) path sampling to accelerate binding-pocket sampling. As proof of principle, we apply SubPEx to three proteins relevant to drug discovery: heat shock protein 90, influenza neuraminidase, and yeast hexokinase 2. SubPEx is available free of charge without registration under the terms of the open-source MIT license: http://durrantlab.com/subpex/.

How far can we stretch the timescale with RETIS?

Molecular dynamics (MD) and Monte Carlo (MC) have long coexisted as two main independent branches of molecular simulation. In the late eighties, however, algorithms based on the combination of both were created such as hybrid Monte Carlo which uses large MD steps as MC moves. An entirely different kind of combination emerged a decade later via the transition path sampling (TPS) method in which MD trajectories are not just part of the MC move, but also form the state space being sampled. Algorithms like replica exchange transition interface sampling (RETIS) exploit this idea to compute reaction rates via a series of TPS simulations. RETIS yields results identical to hypothetical long MD runs, but with exponentially reduced computation time. This perspective describes the RETIS method and discusses recent and future advancements that will enable the study of even longer molecular timescales with reasonable computational resources.

Variational deep learning of equilibrium transition path ensembles.

We present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

Inferring Human Immunodeficiency Virus 1 Proviral Integration Dates With Bayesian Inference.

Human immunodeficiency virus 1 (HIV) proviruses archived in the persistent reservoir currently pose the greatest obstacle to HIV cure due to their evasion of combined antiretroviral therapy and ability to reseed HIV infection. Understanding the dynamics of the HIV persistent reservoir is imperative for discovering a durable HIV cure. Here, we explore Bayesian methods using the software BEAST2 to estimate HIV proviral integration dates. We started with within-host longitudinal HIV sequences collected prior to therapy, along with sequences collected from the persistent reservoir during suppressive therapy. We built a BEAST2 model to estimate integration dates of proviral sequences collected during suppressive therapy, implementing a tip date random walker to adjust the sequence tip dates and a latency-specific prior to inform the dates. To validate our method, we implemented it on both simulated and empirical data sets. Consistent with previous studies, we found that proviral integration dates were spread throughout active infection. Path sampling to select an alternative prior for date estimation in place of the latency-specific prior produced unrealistic results in one empirical data set, whereas on another data set, the latency-specific prior was selected as best fitting. Our Bayesian method outperforms current date estimation techniques with a root mean squared error of 0.89 years on simulated data relative to 1.23-1.89 years with previously developed methods. Bayesian methods offer an adaptable framework for inferring proviral integration dates.

Anytime bottom-up rule learning for large-scale knowledge graph completion

Knowledge graph completion is the task of predicting correct facts that can be expressed by the vocabulary of a given knowledge graph, which are not explicitly stated in that graph. Broadly, there are two main approaches for solving the knowledge graph completion problem. Sub-symbolic approaches embed the nodes and/or edges of a given graph into a low-dimensional vector space and use a scoring function to determine the plausibility of a given fact. Symbolic approaches learn a model that remains within the primary representation of the given knowledge graph. Rule-based approaches are well-known examples. One such approach is AnyBURL. It works by sampling random paths, which are generalized into Horn rules. Previously published results show that the prediction quality of AnyBURL is close to current state of the art with the additional benefit of offering an explanation for a predicted fact. In this paper, we propose several improvements and extensions of AnyBURL. In particular, we focus on AnyBURL’s capability to be successfully applied to large and very large datasets. Overall, we propose four separate extensions: (i) We add to each rule a set of pairwise inequality constraints which enforces that different variables cannot be grounded by the same entities, which results into more appropriate confidence estimations. (ii) We introduce reinforcement learning to guide path sampling in order to use available computational resources more efficiently. (iii) We propose an efficient sampling strategy to approximate the confidence of a rule instead of computing its exact value. (iv) We develop a new multithreaded AnyBURL, which incorporates all previously mentioned modifications. In an experimental study, we show that our approach outperforms both symbolic and sub-symbolic approaches in large-scale knowledge graph completion. It has a higher prediction quality and requires significantly less time and computational resources.

Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation.

Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.

Open-path dual-comb spectroscopy of methane and VOC emissions from an unconventional oil well development in Northern Colorado.

We present results from a field study monitoring methane and volatile organic compound emissions near an unconventional oil well development in Northern Colorado from September 2019 to May 2020 using a mid-infrared dual-comb spectrometer. This instrument allowed quantification of methane, ethane, and propane in a single measurement with high time resolution and integrated path sampling. Using ethane and propane as tracer gases for methane from oil and gas activity, we observed emissions during the drilling, hydraulic fracturing, millout, and flowback phases of well development. Large emissions were seen in drilling and millout phases and emissions decreased to background levels during the flowback phase. Ethane/methane and propane/methane ratios varied widely throughout the observations.

Analysing ill-conditioned Markov chains.

Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Accelerated Entropic Path Sampling with a Bidirectional Generative Adversarial Network.

The role of entropy in mediating the dynamic outcomes of chemical reactions remains largely unknown. To evaluate the change of entropy along post-transition state paths, we have previously developed entropic path sampling that computes configurational entropy from an ensemble of reaction trajectories. However, one major caveat of this approach lies in its high computational demand: about 2000 trajectories are needed to converge the computation of an entropic profile. Here, by leveraging a deep generative model, we developed an accelerated entropic path sampling approach that evaluates entropic profiles using merely a few hundred reaction dynamic trajectories. The new method, called bidirectional generative adversarial network-entropic path sampling, can enhance the estimation of probability density functions of molecular configurations by generating pseudo-molecular configurations that are statistically indistinguishable from the true data. The method was established using cyclopentadiene dimerization, in which we reproduced the reference entropic profiles (derived from 2480 trajectories) using merely 124 trajectories. The method was further benchmarked using three reactions with symmetric post-transition-state bifurcation, including endo-butadiene dimerization, 5-fluoro-1,3-cyclopentadiene dimerization, and 5-methyl-1,3-cyclopentadiene dimerization. The results indicate the existence of a "hidden entropic intermediate", which is a dynamic species that binds to a local entropic maximum where no free energy minimum is formed.

Target-aware Bayesian inference via generalized thermodynamic integration

In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function f(textbf{x}). We consider a target-aware scenario where f(textbf{x}) is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided.

Kinetic reconstruction of free energies as a function of multiple order parameters.

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Machine-guided path sampling to discover mechanisms of molecular self-organization

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

Enhanced comprehensive properties of directed energy deposited Inconel 718 by a novel integrated deposition strategy

Nickel-based superalloys fabricated by wire-arc directed energy deposition, also known as wire arc additive manufacturing (WAAM), usually exhibit inherent columnar grain structure, micro-segregation, and rough surface. A novel deposition strategy, integrating an oscillating arc and forced interlayer cooling, was developed in WAAM of Inconel (IN) 718 components. The influences of deposition modes on geometrical characteristics, defects, microstructure, and mechanical properties were systematically evaluated. The results showed that the oscillation mode, compared to the standard parallel mode, can effectively promote the molten pool's spread and wettability, as well as prevent overflow, finally resulting in high geometric accuracy. In addition, the voids-like defects were reduced by 77.78%, while most common crack defects were not observed. Meanwhile, the forced interlayer cooling process further increased the cooling rate, leading to the reduction of the element segregation as well as the proportion of long-chain-like Laves phases. After a short-process modified heat treatment, the anisotropic mechanical behaviors of the as-deposited samples were almost eliminated. Compared with the parallel mode samples, the yield strength and ultimate tensile strength of the oscillation path samples increased by 5.75% and 9.25%, respectively, while the elongation increased significantly by 51.20%. This signifies that their strength and ductility were simultaneously improved. The strengthening mechanisms were further analyzed based on the distribution of the strengthening phases, as well as the residual Laves phases and porosity.