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DOE OSTI2023

Beam dynamics corrections in the measurement of the anomalous precession frequency at the Muon $g-2$ experiment at Fermilab

The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗

DOE OSTI2017

Variations in annual water-energy balance and their correlations with vegetation and soil moisture dynamics: A case study in the Wei River Basin, China

It is of importance to investigate watershed water-energy balance variations and to explore their correlations with vegetation and soil moisture dynamics, which helps better understand the interplays between underlying surface dynamics and the terrestrial water cycle. The heuristic segmentation method was adopted to identify change points in the parameter to series in Fu's equation belonging to the Budyko framework in the Wei River Basin (WRB) and its sub-basins aiming to examine the validity of stationary assumptions. Additionally, the cross wavelet analysis was applied to explore the correlations between vegetation and soil moisture dynamics and to variations. Results indicated that (1) the omega variations in the WRB are significant, with some change points identified except for the sub-basin above Zhangjiashan, implying that the stationarity of omega series in the WRB is invalid except for the sub-basin above Zhangjiashan; (2) the correlations between soil moisture series and to series are weaker than those between Normalized Difference Vegetation Index (NDVI) series and omega series; (3) vegetation dynamics show significantly negative correlations with omega variations in 1983-2003 with a 4-8 year signal in the whole WRB, and both vegetation and soil moisture dynamics exert strong impacts on the parameter omega changes. This study helps understanding the interactions between underlying land surface dynamics and watershed water-energy balance. (C) 2017 Elsevier B.V. All rights reserved.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Controlling Interfacial Dynamics: Covalent Bonding versus Physical Adsorption in Polymer Nanocomposites

It is generally believed that the strength of the polymer nanoparticle interaction controls the modification of near-interface segmental mobility in polymer nanocomposites (PNCs). However, little is known about the effect of covalent bonding on the segmental dynamics and glass transition of matrix-free polymer-grafted nanoparticles (PGNs), especially when compared to PNCs. In this article, we directly compare the static and dynamic properties of poly(2-vinylpyridine)/silica-based nanocomposites with polymer chains either physically adsorbed (PNCs) or covalently bonded (PGNs) to identical silica nanoparticles (RNP = 12.5 nm) for three different molecular weight (MW) systems. Interestingly, when the MW of the matrix is as low as 6 kg/mol (RNP/Rg = 5.4) or as high as 140 kg/mol (RNP/Rg= 1.13), both small-angle X-ray scattering and broadband dielectric spectroscopy show similar static and dynamic properties for PNCs and PGNs. However, for the intermediate MW of 18 kg/mol (RNP/Rg = 3.16), the difference between physical adsorption and covalent bonding can be clearly identified in the static and dynamic properties of the interfacial layer. We ascribe the differences in the interfacial properties of PNCs and PGNs to changes in chain stretching, as quantified by self-consistent field theory calculations. These results demonstrate that the dynamic suppression at the interface is affected by the chain stretching; that is, it depends on the anisotropy of the segmental conformations, more so than the strength of the interaction, which suggests that the interfacial dynamics can be effectively tuned by the degree of stretching a parameter accessible from the MW or grafting density.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Photoinduced Electron–Nuclear Dynamics of Fullerene and Its Monolayer Networks in Solvated Environments

The recently synthesized monolayer fullerene network in a quasi-hexagonal phase (qHP-C 60 ) exhibits superior electron mobility and optoelectronic properties compared to molecular fullerene (C 60 ), making it highly promising for a variety of applications. However, the microscopic carrier dynamics of qHP-C 60 remain unclear, particularly in realistic environments, which are of significant importance for applications in optoelectronic devices. Unfortunately, traditional ab initio methods are prohibitive for capturing the real-time carrier dynamics of such large systems due to their high computational cost. In this work, we present the first real-time electron–nuclear dynamics study of qHP-C 60 using velocity-gauge density functional tight binding, which enables us to perform several picoseconds of excited-state electron–nuclear dynamics simulations for nanoscale systems with periodic boundary conditions. When applied to C 60 , qHP-C 60 , and their solvated counterparts, we demonstrate that water/moisture significantly increases the electron–hole recombination time in C 60 but has little impact on qHP-C 60 . Our excited-state electron–nuclear dynamics calculations show that qHP-C 60 is extremely unique and enable exploration of time-resolved dynamics for understanding excited-state processes of large systems in complex, solvated environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Water Dynamics in Polyacrylamide Hydrogels

Polymeric hydrogels have wide applications including electrophoresis, biocompatible materials, water superadsorbents, and contact lenses. The properties of hydrogels involve the poorly characterized molecular dynamics of water and solutes trapped within the three-dimensional cross-linked polymer networks. In this study, we apply ultrafast infrared two-dimensional infrared (2D IR) vibrational echo and polarization-selective pump-probe (PSPP) spectroscopies to investigate the ultrafast molecular dynamics of water and a small molecular anion solute, selenocyanate (SeCN - ), in polyacrylamide hydrogels. For all mass concentrations of polymer studied (5% and above), the hydrogen bonding network reorganization (spectral diffusion) dynamics and reorientation dynamics reported by both water and SeCN - solvated by water are significantly slower than in bulk water. As the polymer mass concentration increases, molecular dynamics in the hydrogels slow further. The magnitudes of the slowing, measured with both water and SeCN - , are similar. However, the entire hydrogen bonding network of water molecules appear to slow down as a single ensemble, without a difference between the core water population and the interface water population at the polymer-water surface. In contrast, the dissolved SeCN - do exhibit two-component dynamics, where the major component is assigned to the anions fully solvated in the confined water nanopools. Lastly, the slower component has a small amplitude which is correlated with the polymer mass concentration, and is assigned to adsorbed anions strongly interacting with the polymer fiber networks.

14 SOLAR ENERGY↗

DOE OSTI2023

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density–density and hydrostatic pressure–pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. Furthermore, these results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Energy conservation in real-time nuclear–electronic orbital Ehrenfest dynamics

Real-time nuclear–electronic orbital Ehrenfest (RT-NEO-Ehrenfest) dynamics methods provide a first-principles approach for describing nonadiabatic molecular processes with nuclear quantum effects. For an efficient description of proton transfer within RT-NEO-Ehrenfest dynamics, the basis function center associated with the quantum proton can be allowed to move classically. Here, this traveling proton basis (TPB) approach effectively captures proton quantum dynamics, although its energy conservation behavior is not yet fully satisfactory. Two recently proposed TPB approaches, in principle, conserve the extended energy, which includes both the system energy and the kinetic energy associated with the proton basis function center. Herein, a thermostatted TPB approach is proposed to improve the conservation of the system energy, excluding the kinetic energy associated with the proton basis function center. In this approach, the quantum proton dynamics are modulated by dynamically rescaling the proton momentum operator to maintain the system energy conservation. With the excited-state intramolecular proton transfer of o-hydroxybenzaldehyde as an example, this approach is shown to significantly improve the system energy conservation while preserving the accuracy of the quantum proton dynamics as achieved in the original TPB approach.

Ehrenfest dynamics↗

DOE OSTI2025

Dynamical correlation between ions in liquid seen in real space and time

Controlling ionic transport in liquids is anticipated to provide new scientific and technological opportunities, but it requires accurate knowledge of atomic-scale dynamics of ions beyond the hydrodynamic description. Atomic dynamics in liquids is characterized by strong and dynamical correlations among atoms, which render a conventional approach to describing the dynamics in reciprocal space challenging. We propose an alternative approach to describe liquid dynamics in real space and time using the time-delayed two-body correlation function, Van Hove correlation function, and discuss recent results on the local dynamics in water and electrolytes.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Domain Dynamics under Ultrafast Electric-Field Pulses

Exploring the dynamic responses of a material is of importance to both understanding its fundamental physics at high frequencies and potential device applications. Here we develop a phase-field model for predicting the dynamics of ferroelectric materials and study the dynamic responses of ferroelectric domains and domain walls subjected to an ultrafast electric field pulse. We discover a transition of domain evolution mechanisms from pure domain growth at a relatively low field to combined nucleation and growth of domains at a high field. We derive analytical models for the two regimes which allow us to extract the effective mass and damping coefficient of ferroelectric domain walls. The exhibition of two regimes for the ferroelectric domain dynamics at low and high electric fields is expected to be a general phenomenon that would appear for ferroic domains under other ultrafast stimuli. Finally, the present work also offers a general framework for studying domain dynamics and obtaining fundamental properties of domain walls and thus for manipulating the dynamic functionalities of ferroelectric materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Data-Centric Approach to Capture Non-Polynomial Nonlinear Dynamics

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for applying EDMD to nonlinear problems arising in systems and control. Existing methods either start from a set of dictionary functions and look for the subset that best fits the underlying nonlinear dynamics or rely on machine learning algorithms to “learn” observable functions. Conversely, in this paper, we start from the dynamical system model and lift it through the Lie derivatives, rendering it into a polynomial form. This proposed transformation into a polynomial form is exact and provides an adequate set of observable functions. The strength of the proposed approach is its applicability to a broader class of nonlinear dynamical systems, particularly those with nonpolynomial functions and compositions thereof. Moreover, it retains the physical interpretability of the underlying dynamical system and can be readily integrated into existing numerical libraries. We demonstrate the proposed approach with an application to electric power systems. The modeled system consists of a single generator connected to an infinite bus, where nonlinear terms include sine and cosine functions. The results demonstrate the effectiveness of the proposed procedure in off-attractor nonlinear dynamics for estimation and prediction; the observable functions obtained from the proposed construction outperform methods that use dictionary functions comprising monomials or radial basis functions.

extended dynamic mode decomposition↗

DOE OSTI2020

Effects of pore size on water dynamics in mesoporous silica

Water confined in mesoporous silica plays a central role in its many uses ranging from gas sorption to nanoconfined chemical reactions. Here in this paper, the influence of pore diameter (2.5–5.4 nm) on water hydrogen bond (H-bond) dynamics in MCM41 and SBA15 mesoporous silicas is investigated using femtosecond infrared vibrational spectroscopy and molecular dynamics simulations on selenocyanate (SeCN-) anions dissolved in the pores. As shown recently, SeCN- spectral diffusion is a reliable probe of surrounding water H-bond structural motions. Additionally, the long CN stretch vibrational lifetime facilitates measurement of the full range of confined dynamics, which are much slower than in bulk water. The simulations shed light on quantitative details that are inaccessible from the spatially averaged observables. The dependence of SeCN- orientational relaxation and that of spectral diffusion on the distance from the silica interface are quantitatively described with an exponential decay and a smoothed step-function, respectively. The distance-dependence of both quantities is found to be independent of the diameter of the pores, and the spatial distribution of SeCN- is markedly non-uniform, reaching a maximum between the interface and the pore center. The results indicate that the commonly invoked two-state, or core–shell, model is a more appropriate description of spectral diffusion. Using these insights, we model the full time-dependence of the measured dynamics for all pore sizes and extract the “core” and “shell” dynamical correlation functions and SeCN- spatial probability distributions. The results are critically compared to those for water confined in reverse micelles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗

DOE OSTI2024

Quasi-elastic neutron scattering study on dynamically asymmetric polymer blends

Compatibility between polymers with different glass transition temperatures controls the thermomechanical properties of blends. This work explores the segmental dynamics of poly(methyl acrylate) (PMA) chains when they are blended with polymers of different rigidities and miscibility. Inspired by the intriguing dynamic asymmetry of chains within the interfacial layer of nanoparticles, this study aims to understand dynamic heterogeneity in dynamically asymmetric blends of PMA/poly(methyl methacrylate) (PMMA), PMA/polystyrene (PS), and PMA/poly(ethylene oxide) (PEO) using the differential scanning calorimetry (DSC) and quasi-elastic neutron scattering (QENS) measurements below and above the glass transition temperature of PMMA or PS. Further, results revealed that the segmental jump distance of PMA increased on blending due to volume enhancement. The reduced effective diffusivity of PMA in PMMA is attributed to PMMA's enhanced flexibility (lower characteristic ratio, C ∞ ) and superior interaction (lower ) when compared with the PS environment. The results demonstrate that the chain rigidity and miscibility affect the free volume, interchain cooperativity, and segmental dynamics in dynamically asymmetric blends.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

High-speed X-ray visualization of dynamic crack initiation and propagation in bone

The initiation and propagation of physiological cracks in porcine cortical and cancellous bone under high rate loading were visualized using high-speed synchrotron X-ray phase-contrast imaging (PCI) to characterize their fracture behaviors under dynamic loading conditions. A modified Kolsky compression bar was used to apply dynamic three-point flexural loadings on notched specimens and images of the fracture processes were recorded using a synchronized high-speed synchrotron X-ray imaging set-up. Three-dimensional synchrotron X-ray tomography was conducted to examine the initial microstructure of the bone before high-rate experiments. The experimental results showed that the locations of fracture initiations were not significantly different between the two types of bone. However, the crack velocities in cortical bone were higher than in cancellous bone. Crack deflections at osteonal cement lines, a prime toughening mechanism in bone at low rates, were observed in the cortical bone under dynamic loading in this study. Fracture toughening mechanisms, such as untracked ligament bridging and bridging in crack wake were also observed for the two types of bone. The results also revealed that the fracture toughness of cortical bone was higher than cancellous bone. The crack was deflected to some extent at osteon cement line in cortical bone instead of comparatively penetrating straight through the microstructures in cancellous bone. Statement of Significance Fracture toughness is with great importance to study for crack risk prediction in bone. For those cracks in bone, most of them are associated with impact events, such as sport accidents. Consequently, we visualized, in real-time, the entire processes of dynamic fractures in notched cortical bone and cancellous bone specimens using synchrotron X-ray phase contrast imaging. The onset location of crack initiation was found independent on the bone type. We also found that, although the extent was diminished, crack deflections at osteon cement lines, a major toughening mechanism in transversely orientated cortical bone at quasi-static rate, were still played a role in resisting cracking in dynamically loaded specimen. Furthermore, these finding help researchers to understand the dynamic fracture behaviors in bone.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗

DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗

DOE OSTI2015

A framework for stochastic simulations and visualization of biological electron-transfer dynamics

Electron transfer (ET) dictates a wide variety of energy-conversion processes in biological systems. Visualizing ET dynamics could provide key insight into understanding and possibly controlling these processes. We present a computational framework named VizBET to visualize biological ET dynamics, using an outer-membrane Mtr–Omc cytochrome complex in Shewanella oneidensis MR-1 as an example. Starting from X-ray crystal structures of the constituent cytochromes, molecular dynamics simulations are combined with homology modeling, protein docking, and binding free energy computations to sample the configuration of the complex as well as the change of the free energy associated with ET. This information, along with quantum-mechanical calculations of the electronic coupling, provides inputs to kinetic Monte Carlo (KMC) simulations of ET dynamics in a network of heme groups within the complex. Visualization of the KMC simulation results has been implemented as a plugin to the Visual Molecular Dynamics (VMD) software. Finally, VizBET has been used to reveal the nature of ET dynamics associated with novel nonequilibrium phase transitions in a candidate configuration of the Mtr–Omc complex due to electron–electron interactions.

74 ATOMIC AND MOLECULAR PHYSICS↗