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Fiats: Functional inference and training for surrogates

Fiats provides a platform for research on the training and deployment of neural-network surrogate models for computational science. Fiats also supports exploring, advancing, and combining functional, object-oriented, and parallel programming patterns in Fortran 2023. As such, the Fiats name has dual expansions: “Functional Inference And Training for Surrogates” or “Fortran Inference And Training for Science.” Fiats inference and training procedures are pure and therefore satisfy a language constraint imposed on procedure invocations inside Fortran’s parallel loop construct: do concurrent. Furthermore, the Fiats training procedures are built around a do concurrent parallel reduction. Several compilers can automatically parallelize do concurrent on Central Processing Units (CPUs) or Graphics Processing Units (GPUs). Fiats thus aims to achieve performance portability through standard language mechanisms.

Rouson, Damian [Lawrence Berkeley National Laborat

Novel Results Visualization for Dynamic PSA and New Modeling Features in EMRALD

The Event Modeling Risk Assessment Linked Diagram (EMRALD) tool, developed at the Idaho National Laboratory (INL), was designed to simplify the creation of dynamic models and support various research projects. One of the primary goals of EMRALD was to provide visual methods for modeling. EMRALD consists of two main components: a web-based user interface for model development and a solve engine for running model simulations. Over time, it has evolved to meet the diverse needs of its users. Initially, EMRALD's results were simple text outputs with final key state percentages and uncertainty bounds. However, because EMRALD utilizes a three-phase discrete event simulation and tracks the paths of each simulation run leading to a key state, there is significant potential to analyze large sets of path results data, including state paths, events, and timing. Visualizing this data meaningfully posed a challenge. To address this, a novel time-based Sankey diagram was developed. EMRALD exports results data in a format that can be opened in this Sankey viewer, allowing users to visualize paths, occurrences, events, and probability data for the entire simulation run in a single diagram. Moreover, when EMRALD was first created, there were limited tools capable of meeting its graphical requirements, many of which are no longer supported. In 2024, a new web-based interface was developed using modern graphing tools, enabling additional modeling features. This paper discusses the new dynamic PSA results visualization capability and the enhanced modeling tools available in EMRALD.

97 - MATHEMATICS AND COMPUTING

High-Performance Semiempirical Excited-State Molecular Dynamics Powered by Graphics Processing Units

Here, this Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born–Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM’s PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.

Science & Technology - Other Topics

An Overview of the Molten Salt Thermal Properties Database--Thermophysical, Version 3.1 (MSTDB-TP v.3.1)

This report presents the current status of the Molten Salt Thermal Properties Database–Thermophysical (MSTDB-TP). Information regarding version 3.1 is provided herein, which contains 820 individual salt entries (data from 180+ independent studies); the thermophysical properties contained in the database include density, viscosity, thermal conductivity, and heat capacity. The major updates to the database include a significant expansion of pseudobinary and higher-order chloride salt mixtures, many of which bearing actinides, and an incorporation of more recent literature data (i.e., that within the past 5 years). Also, modifications have been made to the pure compound data in the database as a consequence of an external quality assessment of duplicate datasets. The user-facing API for the MSTDB-TP, Saline, has been updated to include viscosity estimation capabilities based on the Redlich–Kister formalism; this is an advancement with respect to the existing density estimation capabilities. The graphical user interface was also updated to include a density estimation capability, backed by Saline. Finally, additional preliminary efforts to include surface tension into the database, as well as an investigation on formalisms that would be appropriate for thermal conductivity estimation, are reported herein.

36 MATERIALS SCIENCE

Shaping dark photon spectral distortions

The cosmic microwave background (CMB) spectrum is an extraordinary tool for exploring physics beyond the Standard Model. The exquisite precision of its measurement makes it particularly sensitive to small effects caused by hidden sector interactions. In particular, CMB spectral distortions can unveil the existence of dark photons which are kinetically coupled to the standard photon. In this work, we use the COBE-FIRAS dataset to derive accurate and robust limits on photon-to-dark-photon oscillations for a large range of dark photon masses, from 10$^{−10}$ to 10$^{−4}$ eV. We consider in detail the redshift dependence of the bounds, computing CMB distortions due to photon injection/removal using a Green’s function method. Our treatment improves on previous results, which had set limits studying energy injection/removal into baryons rather than photon injection/removal, or ignoring the redshift evolution of distortions. The difference between our treatment and previous ones is particularly noticeable in the predicted spectral shape of the distortions, a smoking gun signature for photon-to-dark-photon oscillations. The characterization of the spectral shape is crucial for future CMB missions, which could improve the present sensitivity by orders of magnitude, exploring regions of the dark photon parameter space that are otherwise difficult to access [inline-graphic not available: see fulltext].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

3-center and 4-center 2-particle Gaussian AO integrals on modern accelerated processors

We report an implementation of the McMurchie–Davidson (MD) algorithm for 3-center and 4-center 2-particle integrals over Gaussian atomic orbitals (AOs) with low and high angular momenta l and varying degrees of contraction for graphical processing units (GPUs). This work builds upon our recent implementation of a matrix form of the MD algorithm that is efficient for GPU evaluation of 4-center 2-particle integrals over Gaussian AOs of high angular momenta (l ≥ 4) [A. Asadchev and E. F. Valeev, J. Phys. Chem. A 127, 10889–10895 (2023)]. The use of unconventional data layouts and three variants of the MD algorithm allow for the evaluation of integrals with double precision and sustained performance between 25% and 70% of the theoretical hardware peak. Performance assessment includes integrals over AOs with l ≤ 6 (a higher l is supported). Preliminary implementation of the Hartree–Fock exchange operator is presented and assessed for computations with up to a quadruple-zeta basis and more than 20 000 AOs. The corresponding C++ code is part of the experimental open-source LibintX library available at https://github.com/ValeevGroup/libintx.

Chemistry

Measurement of the Zγ production cross section and search for anomalous neutral triple gauge couplings in pp collisions at $ \sqrt{s}=13 $ TeV

A measurement of the fiducial cross section of the associated production of a Z boson and a high-p$_{T}$ photon, where the Z decays to two neutrinos, and a search for anomalous triple gauge couplings are reported. The results are based on data collected by the CMS experiment at the LHC in proton-proton collisions at $ \sqrt{s}=13 $ TeV during 2016-2018, corresponding to an integrated luminosity of 138 fb$^{−1}$. The fiducial Zγ cross section, where a photon with a p$_{T}$ greater than 225 GeV is produced in association with a Z, and the Z decays to a $ \upnu \overline{\upnu} $ pair $ \left(\mathrm{Z}\left(\upnu \overline{\upnu}\right)\upgamma \right) $, is measured to be $ {23.3}_{-1.3}^{+1.4} $ fb, in agreement, within uncertainties, with the standard model prediction. The differential cross section as a function of the photon p$_{T}$ has been measured and compared with standard model predictions computed at next-to-leading and at next-to-next-to-leading order in perturbative quantum chromodynamics. Constraints have been placed on the presence of anomalous couplings that affect the ZZγ and Zγγ vertex using the p$_{T}$ spectrum of the photons. The observed 95% confidence level intervals for CP-conserving $ {h}_3^{\upgamma} $ and $ {h}_4^{\upgamma} $ are determined to be (−3.4, 3.5)×10$^{−4}$ and (−6.8, 6.8)×10$^{−7}$, and for $ {h}_3^{\mathrm{Z}} $ and $ {h}_4^{\mathrm{Z}} $ they are (−2.2, 2.2)×10$^{−4}$ and (−4.1, 4.2)×10$^{−7}$, respectively. These are the strictest limits to date on $ {h}_3^{\upgamma} $, $ {h}_3^{\mathrm{Z}} $ and $ {h}_4^{\mathrm{Z}} $.[graphic not available: see fulltext]

Hayrapetyan, Aram [Yerevan Phys. Inst.]

An open-access simulated earthquake ground-motion database for an M7 Hayward Fault earthquake in the San Francisco Bay Region

Comprehensive understanding of earthquake ground motions, particularly in the near-fault region of large-magnitude events, is limited by gaps in strong-motion data. This challenge is prominent in areas with high seismic hazard but infrequent large earthquakes where data is sparse and difficult to interpret. These data limitations lead to uncertainties in the development of site-specific ground motions, which are crucial for engineering risk assessments. To address these challenges, physics-based regional-scale ground-motion simulations have been developed. With the emergence of exaflop-scale computing ecosystems, it is now possible to simulate regional earthquake processes at unprecedented fidelity and generate the large number of fault rupture realizations necessary to characterize both intra- and inter-event ground-motion variability. This article introduces a new database of simulated earthquake ground motions, created for applications in earthquake engineering, earthquake planning, and emergency response. The inaugural version of the database features simulated ground motions for a magnitude 7 Hayward Fault earthquake in the San Francisco Bay Region (SFBR), using the EarthQuake SIMulation (EQSIM) simulation framework and the Graves–Pitarka kinematic rupture model. The aim is to provide high-fidelity, spatially dense, three-component motions generated on the Department of Energy’s (DOE) newest generation of graphics processing unit (GPU)-accelerated supercomputers. These motions are being made openly available to the engineering, scientific, and disaster planning communities. In addition, this work develops protocols for the efficient dissemination of these large data sets and emphasizes community engagement to build confidence in their application. This article discusses the methodology behind the data, underlying software verification and validation, scalable data management, and a user interface for data access. The goal is to facilitate widespread use and elicit expert feedback to maximize the utility and exploitation of simulated motions. While the initial focus is on the San Francisco Region, simulations for additional regions will be added as the DOE program progresses.

Simulated ground-motion database

Improving the User Interface of the DeepLynx Data Warehouse

DeepLynx is an open-source ontology-based data warehouse created by INL to support the creation and life cycle of digital engineering projects, with a particular emphasis on digital twins [1]. Digital twins are systems that represent physical assets and process in a real-time digital environment [1]. Most well-known commercial data warehouses use Graphical User Interfaces (GUIs) for users to interact with their systems [3]. Limited publications have addressed the design of these interfaces and understanding of their target users. The current users and development team acknowledge the need to improve the current UI, not just for aesthetics but to improve functionality and workflow of DeepLynx. Traditional data warehouse users are developers, data scientists and business analysts [2]. DeepLynx users have a vast range of experience using data warehouses, and diverse roles, including engineers, scientists and management positions. Because there is a broader audience of target users for DeepLynx than a typical data warehouse, it is essential that DeepLynx has a useable and intuitive user interface. To achieve this the team performed human-computer interaction methods, including a Heuristic Evaluation of current UI using Neilsen’s Usability Heuristic, create personas based on current users by designing a user survey, data analysis and develop of personas. Followed by a redesign of the UI following using Neilsen’s Usability Heuristic and Norman’s Principles of Interactive Design in industry standard software Figma. Lastly a Heuristic Evaluation of new UI design, using Neilsen’s Usability Heuristic and User testing of redesign UI and have a group of users complete a Thinking Aloud Test of the new UI. Preliminary results of the Heuristic Evaluation of current UI arise issue with Consistency and Standards, Visibility of System Status, Match System and Real World and Recognition Rather than Recall. These issues were addressed in the proposed redesign by applying Neilsen’s Usability Heuristic and Norman’s Principles of Interactive Design. Next steps include formalized list of lessons learned and design implications for future publications.

97 MATHEMATICS AND COMPUTING

INSPIRED: Inelastic neutron scattering prediction for instantaneous results and experimental design

Inelastic neutron scattering (INS) has unique advantages in probing how atoms vibrate and how the vibrations propagate and interact. Such dynamic information is crucial in understanding various material properties, from heat capacity, thermal conductivity, phase transitions, and chemical reactions to more exotic quantum behavior. The analysis and interpretation of the INS spectra often start from a model structure of the sample, followed by a series of calculations to obtain the simulated spectra to compare with experiments. The conventional way to perform such calculations usually requires significant time, computing resources, and specialized expertise. Here, we present a new program named INSPIRED (Inelastic Neutron Scattering Prediction for Instantaneous Results and Experimental Design), which enables users to perform rapid INS simulations in several different ways on their personal computers in just a few clicks, with the crystal structure as the only input file. Specifically, the users can choose a pre-trained symmetry-aware neural network (coupled with an autoencoder) to predict the phonon density of states (DOS), 1D S(E) and 2D S(|Q|,E) spectra for any given structure. One can also choose an existing density functional theory (DFT) calculation from a database (containing over 12,000 crystals), and quickly obtain the simulated INS spectra for single crystals and powders. It is also possible to use pre-trained universal machine learning force fields to relax a given crystal structure, calculate the phonon dispersion and DOS, and, subsequently, the INS spectra. All these functions are implemented with a PyQt graphic user interface. Finally, we expect these new tools will benefit broad user communities and significantly improve the efficiency of experiment design, execution, and data analysis for INS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

GADRAS-DRF Enhancements for Safeguards – Custom Peak Fitting to Enhance Model Fitting and Isotopics

One major software update was accomplished within the Gamma Detector Response and Analysis Software-Detector Response Function (GADRAS-DRF) package. This update allows users to adjust individual peak fits for use in subsequent analysis processes within GADRAS-DRF. A graphical user interface (GUI) was implemented so users can see the effect of their fit adjustments on the spectrum. This new feature will enhance the capability of the previously funded auto-enrichment and peak-based 1D model fit feature that was implemented in FY23 (Fiscal Year). Isotopic analysis was performed using M400 data obtained from uranium standards and the isotopic assessment is given with and without manual peak adjustments.

07 ISOTOPE AND RADIATION SOURCES

An Overview of the Molten Salt Thermal Properties Database–Thermophysical, Version 4.0 (MSTDB-TP V.4.0)

A central repository of thermophysical and thermochemical properties of molten salt compositions of relevance to molten salt reactors (MSRs) is vital in supporting the broad community of MSR developers, who are at various stages of developing and deploying their reactor designs. In general, these MSR designs differ significantly from developer to developer (e.g., with respect to the hardness of the neutron spectra, level of fissile loading, target multicomponent temperatures and power levels, and moderating capabilities). Therefore, the fuel and coolant salts being considered vary greatly: they may be chlorides or fluorides, they utilize different actinides at different ratios, and the cations in the melt are selected based on perceived advantages and disadvantages. Considering the general need for thermal properties, and the vastness of the array of potential candidate salt mixtures, the Molten Salt Thermal Properties Database (MSTDB) was initiated in 2018 with the goal of providing thermophysical and thermochemical characterization of key molten salt compounds and mixtures across their temperature and compositional domains. The MSTDB is thus divided into the thermophysical arm (MSTDB-TP) and the thermochemical arm (MSTDB-TC). The MSTDB is an effort funded by the Department of Energy, Office of Nuclear Energy (DOE-NE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, and the MSR Campaign. This report provides an overview of the MSTDB-TP v4.0 in terms of the data contained within, the state of the tools used to access the data, the availability of predictive models that leverage the raw data in the database, the preliminary status of developmental efforts that are currently underway, and an account of future goals for MSTDB-TP. The primary goal for the update from MSTDB-TP v.3.1 to v4.0 was the incorporation of surface tension data into the database; this property is important for thermal hydraulics modeling and species transport in other tools that have been developed under the NEAMS program. A breakdown of the surface tension data that have been added into MSTDB-TP v4.0 is provided herein, and the manner in which the quality of the data has been assessed is also documented. For MSTDB-TP v4.0, newly published thermophysical property data—primarily from collaborative experimental efforts under the MSR Campaign—have been incorporated into the database, and the resulting expansion is documented here. Because of the size to which MSTDB-TP has grown, the raw data format has now been recast into JavaScript Object Notation (JSON) format for easier connection with the MSTDB-TP application programming interface (API). Saline; the pre-existing comma-separated value (CSV) format has been deprecated but is still maintained, accessible, and up to date. As a final effort in packaging the MSTDB-TP v4.0 update, the graphical user interface (GUI) for MSTDB has been updated to allow full accessibility to the density and viscosity predictive models, which are based on Redlich-Kister expansions of MSTDB-TP raw data. Some other major aspects of this report, in terms of preliminary and future work, include: (1) documentation of the formalism and preliminary testing of a kinetic theory model that may act as a predictive model for thermal conductivity; (2) documentation of the candidate predictive models that may be considered in the future for surface tension, making use of the surface tension data now in MSTDB-TP v4.0; (3) a preliminary account of a data collection process that will enable the filling of additional gaps within MSTDB-TP, namely with data which have been collected computationally (e.g., through ab initio molecular dynamics).

22 GENERAL STUDIES OF NUCLEAR REACTORS

Road Lidar Dataset for the TxDOT Austin District

This is a road lidar data collection for developing road elevation models and road inundation mapping methodologies, a joint work between ORNL and The University of Texas at Austin. This dataset is generated as part of the flood transportation infrastructure, partly funded by the NOAA CIROH project. ORNL is a project partner for high-performance computing-empowered flood inundation mapping methodology R&D. The dataset is computed using a GPU-accelerated lidar data processing workflow developed at ORNL. The lidar data source is from TxGIO, the state lidar data collection site. The output dataset is in two formats: laz and copc. It is organized by TxDOT's maintenance sections, covering the Austin District. Data size: 3.86 billion road lidar points, 1.67% of the entire lidar data input Projection: EPSG:32614 (WGS84/UTM zone 14N) Website: https://web.corral.tacc.utexas.edu/nfiedata/road3d/austin_district/AustinMaintenanceSections_H_epsg6343_V_epsg5703/ LICENSE FOR USE -- MAPS AND DATA DISCLAIMER This resource is shared under the Creative Commons Attribution CC BY, http://creativecommons.org/licenses/by/4.0/ MAPS AND DATA DISCLAIMER The Oak Ridge National Laboratory (ORNL) shall not be held liable for improper or incorrect use of the data described or information contained on this map or associated series of maps. The data and related map graphics are not legal, land survey or engineering documents and are not intended to be used as such. ORNL gives no warranty, express or implied, as to the accuracy, reliability, utility or completeness of this information. The user of these maps and data assumes all responsibility and risk for the use of the maps and data. ORNL disclaims all warranties, representations or endorsements either express or implied, with regard to the information contained in this map product, including, but not limited to, all implied warranties of merchantability, fitness for a particular purpose or non-infringement. This preliminary map product is for research and review purposes only. It is not intended to be used for emergency management operational or life safety decisions at the local or regional governmental level or by the general public. Users requiring information regarding hazardous conditions or meteorological conditions for specific geographic areas should consult directly with their city or county emergency management office.

54 ENVIRONMENTAL SCIENCES

Bayesian chain graph models to characterize microbe-environment dynamics

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data.

compositional data

Refining HPCToolkit for application performance analysis at exascale

As part of the US Department of Energy’s Exascale Computing Project (ECP), Rice University has been refining its HPCToolkit performance tools to better support measurement and analysis of applications executing on exascale supercomputers. To efficiently collect performance measurements of GPU-accelerated applications, HPCToolkit employs novel non-blocking data structures to communicate performance measurements between tool threads and application threads. To attribute performance information in detail to source lines, loop nests, and inlined call chains, HPCToolkit performs parallel analysis of large CPU and GPU binaries involved in the execution of an exascale application to rapidly recover mappings between machine instructions and source code. To analyze terabytes of performance measurements gathered during executions at exascale, HPCToolkit employs distributed-memory parallelism, multithreading, sparse data structures, and out-of-core streaming analysis algorithms. To support interactive exploration of profiles up to terabytes in size, HPCToolkit’s hpcviewer graphical user interface uses out-of-core methods to visualize performance data. The result of these efforts is that HPCToolkit now supports collection, analysis, and presentation of profiles and traces of GPU-accelerated applications at exascale. These improvements have enabled HPCToolkit to efficiently measure, analyze and explore terabytes of performance data for executions using as many as 64K MPI ranks and 64K GPU tiles on ORNL’s Frontier supercomputer. HPCToolkit’s support for measurement and analysis of GPU-accelerated applications has been employed to study a collection of open-science applications developed as part of ECP. This paper reports on these experiences, which provided insight into opportunities for tuning applications, strengths and weaknesses of HPCToolkit itself, as well as unexpected behaviors in executions at exascale.

Adhianto, Laksono

jaxhps: An elliptic PDE solver built with machine learning in mind

Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver may be required to generate a training dataset, run in the inner loop of an iterative algorithm, or interface directly with a deep neural network. To provide value to machine learning users, such a PDE solver must be compatible with standard automatic differentiation frameworks, scale efficiently when run on graphics processing units (GPUs), and maintain high accuracy for a large range of input parameters. We have designed the jaxhps package with these use-cases in mind by implementing a highly efficient and accurate solver for elliptic problems with native hardware acceleration and automatic differentiation support.

97 MATHEMATICS AND COMPUTING

Unifying Combinatorial and Graphical Methods in Artificial Intelligence

Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).

97 MATHEMATICS AND COMPUTING