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464 records · Page 26

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials using MALAMUTE

The Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy aims to develop and qualify additively manufactured materials for nuclear applications. One key challenge to this is the microstructural variability observed in the additively manufactured products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-throughput experimental and modeling techniques to accelerate qualification. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the additive manufacturing process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture microstructural variability is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning models to develop a digital twin for additive manufacturing that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation. The melting and subsequent solidification that occurs during the additive process is a complex phenomenon that requires multiscale multiphysics analysis. This work package focuses on understanding the role of process variabilities on the unique microstructural characteristics of additively manufactured materials. Microstructural features at the subgrain level, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. Idaho National Laboratory’s Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for additively manufactured materials in an efficient, reliable, and cost-effective way. This work focuses on capturing the microstructural variabilities at the subgrain level that are often missing in the part-scale models. In fiscal year 2025, we significantly advanced upon our work in the last fiscal year, in terms of the predictive capabilities of the physics-based and ML models, by adding the capabilities to capture subgrain-level micro-segregation during solidification using phase-field model and to predict the time-dependent dynamics of the AM process through the MOGPAR model. The alloy solidification model in MOOSE incorporates the thermodynamic properties and free energy relevant to 316 stainless steel. The model demonstrates the Cr and Ni segregation that occurs during solidification, including that the rate of solidification. The microstructural evolution model is connected to the process conditions via the surrogate model developed in this work. This enables predictions of the final microstructure in conjunctions with the manufacturing process. This work supports AMMT's rapid qualification goals by laying the foundation for an efficient and cost-effective model establishing the PSPP correlation for AM. The generated microstructures and predicted micro-segregation can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work helps to identify the key microstructural features at the subgrain level that are significant in property and performance predictions of additively manufactured components. This work will also provide inputs to the large-scale process variability models to reevaluate and validate assumptions and simplifications made in the part-scale models. Furthermore, through active learning this work can help identify the data need from both modeling and experimental sides for development of a robust digital twin for additive manufacturing and accelerate the AMMT's qualification efforts.

36 - MATERIALS SCIENCE↗

Atomate2: modular workflows for materials science

High-throughput density functional theory (DFT) calculations have become a vital element of computational materials science, enabling materials screening, property database generation, and training of “universal” machine learning models. While several software frameworks have emerged to support these computational efforts, new developments such as machine learned force fields have increased demands for more flexible and programmable workflow solutions. This manuscript introduces atomate2, a comprehensive evolution of our original atomate framework, designed to address existing limitations in computational materials research infrastructure. Key features include the support for multiple electronic structure packages and interoperability between them, along with generalizable workflows that can be written in an abstract form irrespective of the DFT package or machine learning force field used within them. Our hope is that atomate2's improved usability and extensibility can reduce technical barriers for high-throughput research workflows and facilitate the rapid adoption of emerging methods in computational material science.

97 MATHEMATICS AND COMPUTING↗

Constellation: The autonomous control and data acquisition system for dynamic experimental setups

The operation of instruments and detectors in laboratory or beamline environments presents a complex challenge, requiring stable operation of multiple concurrent devices, often controlled by separate hardware and software solutions. These environments frequently undergo modifications, such as the inclusion of different auxiliary devices depending on the experiment or facility, adding further complexity. The successful management of such dynamic configurations demands a flexible and robust system capable of controlling data acquisition, monitoring experimental setups, enabling seamless reconfiguration, and integrating new devices with limited effort. This paper presents Constellation, a flexible and network-distributed control and data acquisition software framework tailored to laboratory and beamline environments, that addresses the limitations of existing solutions. The framework is designed with a focus on extensibility, providing a streamlined interface for instrument integration. It supports efficient system setup via network discovery mechanisms, promotes stability through autonomous operational features, and provides comprehensive documentation and supporting tools for operators and application developers such as controllers and logging interfaces. At the core of the architectural design is the autonomy of the individual components, called satellites, which can make independent decisions about their operation and communicate these decisions to other components. This paper introduces the design principles and framework architecture of Constellation, presents the available graphical user interfaces, shares insights from initial successful deployments, and provides an outlook on future developments and applications.

Autonomy↗

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗

Coupling Microstructural Evolution Simulations to Material Property Degradation Predictions for Plasma-Facing Materials

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500 C to 1500 C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 D/m^2-s. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

Connect microstructure evolution to property degradation with validated simulation

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500$^o$C to 1500$^o$C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 $\frac{D}{m^2s}$. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

Development and Experimental Optimization of High-Temperature Modeling Tools and Methods for Concentrated Solar Power Particle - Systems

A novel, open-source radiative modeling toolset was developed to extend the functionality of particle-based modeling software (e.g. discrete element method (DEM)) to environmental conditions relevant to concentrated solar power applications. This toolset was optimized for deployment on desktop workstations instead of high-performance computing systems, to render such tools more accessible to the research community. Both particle-based modeling and radiative exchange modeling are computationally expensive and often require specialized programming expertise, making these methods cumbersome to use. Recent developments in DEM software by DCS Computing have greatly reduced these challenges, providing a graphical-user-interface based platform and modeling optimization for desktop workstations, HPCs, and cloud computing. The University of Dayton leveraged the experience of DCS Computing in developing a user-friendly, open-source radiative heat transfer expansion for DEM modeling. The University of Dayton DEM+ radiative modeling toolset was developed using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures and flow conditions. The toolset provides researchers with access to multiple radiative models including an accelerated Monte-Carlo Ray Tracing (application agnostic, highly computationally expensive), an expanded database of distance-based approximations (application limited, computationally light), and a weighted blending of the two methods capable of achieving over 90% reduction in computation time with equivalent accuracy compared to Monte-Carlo Ray Tracing. Through a graphical user interface, users can customize the radiative models to match their desired accuracy and available computational resources, improving access to particle based modeling for the research community. Ceramic sintered bauxite proppants were used in modeling and experimentally as a baseline. Both the radiative heat transfer and flow properties for particulate systems were investigated at elevated temperatures up to 800 °C. The major accomplishments for this work include a verified, open-source radiative modeling toolset to be distributed amongst the research community and the fabrication of three small-scale test facilities to investigate particle behavior and tune DEM flow properties for operation up to 800 °C. The findings have been shared with the research community via conference modeling workshops, deployment of the tools in DCS Computing Aspherix®, and open-source access to the developed radiative modeling tool. The development of next-generation CSP facilities and thermal energy storage systems based on ceramic particles requires providing access to computationally efficient and accurate modeling tools. Particles will experience a wide range of environments (20-800 °C) and handling conditions (dilute curtains or dense packing), requiring specially designed and optimized equipment. Optimizing solid particle physics models and establishing best-practices for particle modeling in CSP environments will assist researchers with designing optimized equipment, accelerating the deployment of more economically-competitive CSP facilities.

14 SOLAR ENERGY↗

Design, Preparation, and Execution of the 100-AV Field Test for the CIRCLES Consortium: Methodology and Implementation of the Largest Mobile Traffic Control Experiment to Date

This article presents the comprehensive design, setup, execution, and evaluation of the MegaVanderTest (MVT) experiment conducted by the Congestion Impacts Reduction via CAV-in-the-Loop Lagrangian Energy Smoothing (CIRCLES) Consortium, which aimed to mitigate traffic congestion using partially autonomous vehicles (AVs) (see “Summary”). The experiment involved 100 vehicles on Nashville’s Interstate 24 (I-24) highway, utilizing various control algorithms to smooth stop-and-go traffic waves. The execution of the MVT experiment required a coordinated effort from multiple teams. This article details the meticulous planning process, the coordinated efforts of multiple teams, and the innovative use of a dynamic agent-based simulation framework for traffic evaluation. Here, the contributions of this work include demonstrating and providing a detailed roadmap for large-scale live traffic experiments, illustrating the lessons learned from the MVT experiment, and introducing the other articles in this issue and their complementary relationship in the MVT experiment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Denoising Seismograms in the Time Domain Using a Deep Learning Model

Deep learning has emerged as a transformative tool for enhancing the extraction of reliable information from seismograms, addressing the increasing demand for precise and efficient seismic data analysis. We introduce an innovative encoder–decoder deep learning model, named WaveDenoiser, designed for noise reduction in the time domain, thereby eliminating the need for spectrogram computations that have been used for existing deep learning tools and significantly improving processing speed. Utilizing the benchmark dataset that is Stanford Earthquake Dataset, we developed three models of varying sizes: base, medium, and large. Notably, the large (referred to as WaveDenoiser) model demonstrated superior performance, achieving a median signal‐to‐noise ratio improvement of 8.8 dB on in‐distribution unseen data (in the same geographic region) and 7.7 dB on out‐distribution unseen data (in a new geographic region), outpacing both the base and medium models. Further evaluation of the WaveDenoiser model revealed a reduction in median arrival‐time errors by 0.02 s for P waves and 0.01 s for S waves when processing waveforms prior to phase picking using PhaseNet on in‐distribution unseen data. When tested on out‐distribution unseen data, the model also effectively reduced the P‐wave median arrival‐time error by 0.02 and 0.01 s in median arrival‐time error for S waves. Importantly, the application of WaveDenoiser resulted in a significant reduction of phase picking outliers by 1.1% to 3.6% for both P and S waves. In addition, we achieved over five times acceleration in processing speed compared with the seisBench implementation of DeepDenoiser. Our findings underscore the potential of WaveDenoiser as a powerful tool for improving seismic data analysis and processing efficiency.

P-waves↗

Synthesis of Correct Digital Controller Models from Specifications by Model Transformation (21-0320)

The design of high consequence controllers (in weapons systems, autonomy, etc.) that do what they are supposed to do is a significant challenge. Testing simply does not come close to meeting the requirements for assurance. Today circuit designers at Sandia (and elsewhere) typically capture the core behavior of their components using state models in tools such as STATEFLOW. They then check that their models meet certain requirements (e.g. “The system bus must not deadlock” or “both traffic lights at an intersection must not be green at the same time”) using tools called model checkers. If the model checker returns “yes” then the property is guaranteed to be satisfied by the model. However, there are several drawbacks to this industry practice: (1) there is a lot of detail to get right, this is particularly challenging when there are multiple components requiring complex coordination (2) any errors returned by the model checker have to be traced back through the design and fixed, necessitating rework, (3) there are severe scalability problems with this approach, particularly when dealing with concurrency. All this places high demands on the designers who now face not only an accelerated schedule but also controllers of increasing complexity. This report describes a new and fundamentally different approach to the construction of safety-critical digital controllers. Instead of directly constructing a complete model and then trying to verify it, the designer can start with an initial abstract (think “sketch”) model plus the requirements, from which a correct concrete model is automatically synthesized. There is no need for post-hoc verification of required functional properties. Having tool to carry this out will significantly impact the nation’s ability to ensure the safety of high-consequence digital systems. The approach has been implemented in a prototype tool, along with a suite of examples, including ones that reflect actual problems faced by designers. Our approach operates on a variant of Statecharts developed at Sandia called Qspecs. Statecharts are a widely used formalism for developing concurrent reactive systems, supporting scalability through allowing state models containing composite states, which are the serial or parallel composition of substates which can themselves contain statecharts. Statecharts enable an incremental style of development, in which states are progressively refined to incorporate greater detail in an incremental model of software development. Our approach formulates a set of constraints from the structure of the models and the requirements and propagates these constraints to a fixpoint. The solution to the constraints is an inductive invariant along with guards on the transitions. We also show how our approach extends to implementation refinement, decomposition, composition, and elaboration. We currently handle safety requirements written in LTL (Linear Temporal Logic)

42 ENGINEERING↗

BuildingSync® v.2.7.0 (released 9.11.2025) [SWR-18-28]

BuildingSync® is a building data exchange schema to better enable integration between software tools and building data workflows. The schema's original use case was focused on commercial building energy audits; however, several additional use cases have been realized including building energy modeling and more high-level generic building data exchange. Version 2.7.0 adds new elements for file attachment feature and FederalBuilding, and generalizes usage of Optional Elements (e.g. EquipmentCondition, EquipmentID) to all assets/systems. BuildingSync helps streamline the data exchange process, improving the value of the data, minimizing duplication of effort for subsequent building data collection efforts (including audits), and facilitating the achievement of greater energy efficiency. This in done in part by standardizing on (a) reporting audits in an electronic format, (b) tracking proposed, implemented, and discarded energy conservation measures, and (c) storing building characteristics (at multiple levels) for audits, benchmarking, and building energy analysis. BuildingSync has several documents and tools available to help users understand how to best leverage BuildingSync. The list below are only a subset of the resources available. If new resources are discovered, then feel free to create a new pull request with the additions. Generic BuildingSync information is available on the DOE website and the project website. BuildingSync Examples - These examples are kept up to date and show a wide range of implementations. Any new update to BuildingSync is required to pass validation on these example files. BuildingSync Use Case Validator allows for users to determine if their instance complies with a specific use case for BuildingSync by checking if the required elements are implemented in an uploaded instance. An API is also provided for automated integration into other tools. Also, the website contains an easy way to view the entirety of the schema and how elements relate to the Building Exchange Data Exchange Specification. The Validator is open sourced here Use Case TestSuite provides a Python package for easier generation of BuildingSync use cases. BuildingSync use cases depend on the generation of schematron documents, which is time-consuming and difficult to implement well. The TestSuite allows users to define a use case using a more palatable CSV template, which it then turns into a Schematron document. The source code is available here. BuildingSync to OpenStudio/EnergyPlus. The translator is open sourced here. This project will translate a Level 1 (and partial Level 2) ASHRAE Energy Audit to a fully defined OpenStudio and EnergyPlus model. This project is in early Beta testing and any feedback is welcome!

Long, Nicholas [National Renewable Energy Lab. (NR↗

Archetype-based Redshift Estimation for the Dark Energy Spectroscopic Instrument Survey

We present a computationally efficient galaxy archetype-based redshift estimation and spectral classification method for the Dark Energy Survey Instrument (DESI) survey. The DESI survey currently relies on a redshift fitter and spectral classifier using a linear combination of principal component analysis–derived templates, which is very efficient in processing large volumes of DESI spectra within a short time frame. However, this method occasionally yields unphysical model fits for galaxies and fails to adequately absorb calibration errors that may still be occasionally visible in the reduced spectra. Our proposed approach improves upon this existing method by refitting the spectra with carefully generated physical galaxy archetypes combined with additional terms designed to absorb data reduction defects and provide more physical models to the DESI spectra. We test our method on an extensive data set derived from the survey validation (SV) and Year 1 (Y1) data of DESI. Our findings indicate that the new method delivers marginally better redshift success for SV tiles while reducing catastrophic redshift failure by 10%–30%. At the same time, results from millions of targets from the main survey show that our model has relatively higher redshift success and purity rates (0.5%–0.8% higher) for galaxy targets while having similar success for QSOs. These improvements also demonstrate that the main DESI redshift pipeline is generally robust. Additionally, it reduces the false-positive redshift estimation by 5%–40% for sky fibers. We also discuss the generic nature of our method and how it can be extended to other large spectroscopic surveys, along with possible future improvements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Track reconstruction as a service for collider physics

Optimizing charged-particle track reconstruction algorithms is crucial for efficient event reconstruction in Large Hadron Collider (LHC) experiments due to their significant computational demands. Existing track reconstruction algorithms have been adapted to run on massively parallel coprocessors, such as graphics processing units (GPUs), to reduce processing time. Nevertheless, challenges remain in fully harnessing the computational capacity of coprocessors in a scalable and non-disruptive manner. This paper proposes an inference-as-a-service approach for particle tracking in high energy physics experiments. To evaluate the efficacy of this approach, two distinct tracking algorithms are tested: Patatrack, a rule-based algorithm, and Exa.TrkX, a machine learning-based algorithm. The as-a-service implementations show enhanced GPU utilization and can process requests from multiple CPU cores concurrently without increasing per-request latency. The impact of data transfer is minimal and insignificant compared to running on local coprocessors. This approach greatly improves the computational efficiency of charged particle tracking, providing a solution to the computing challenges anticipated in the High-Luminosity LHC era.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that the interpretable nature of language often provides a much richer learning medium for LLMs, compared to policy gradients derived from sparse, scalar rewards. To test this, we introduce GEPA (Genetic-Pareto), a prompt optimizer that thoroughly incorporates natural language reflection to learn high-level rules from trial and error. Given any AI system containing one or more LLM prompts, GEPA samples trajectories (e.g., reasoning, tool calls, and tool outputs) and reflects on them in natural language to diagnose problems, propose and test prompt updates, and combine complementary lessons from the Pareto frontier of its own attempts. As a result of GEPA's design, it can often turn even just a few rollouts into a large quality gain. Across six tasks, GEPA outperforms GRPO by 6% on average and by up to 20%, while using up to 35x fewer rollouts. GEPA also outperforms the leading prompt optimizer, MIPROv2, by over 10% (e.g., +12% accuracy on AIME-2025), and demonstrates promising results as an inference-time search strategy for code optimization. We release our code at https://github.com/gepa-ai/gepa.

97 MATHEMATICS AND COMPUTING↗