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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Authors:
Nathaniel S. Woodward,
Zhiqi Gao,
Yurii Kvasiuk,
Kendrick M. Smith,
Frederic Sala,
Moritz Münchmeyer
Abstract:
Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiabl…
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Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiable training data required to train such capabilities is scarce, we developed a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting Quantum Field Theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. We perform an extensive analysis of model chains-of-though before and after fine-tuning, to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and $\sim$200M tokens of QFT reasoning traces.
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Submitted 20 April, 2026;
originally announced April 2026.
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Online Navigation Planning for Long-term Autonomous Operation of Underwater Gliders
Authors:
Victor-Alexandru Darvariu,
Charlotte Z. Reed,
Jan Stratmann,
Bruno Lacerda,
Benjamin Allsup,
Stephen Woodward,
Elizabeth Siddle,
Trishna Saeharaseelan,
Owain Jones,
Dan Jones,
Tobias Ferreira,
Chloe Baker,
Kevin Chaplin,
James Kirk,
Ashley Iceton-Morris,
Ryan D. Patmore,
Jeff Polton,
Charlotte Williams,
Christopher D. J. Auckland,
Rob A. Hall,
Alexandra Kokkinaki,
Alvaro Lorenzo Lopez,
Justin J. H. Buck,
Nick Hawes
Abstract:
Underwater glider robots have become indispensable for ocean sampling, yet fully autonomous long-term operation remains rare in practice. Although stakeholders are calling for tools to manage increasingly large fleets of gliders, existing methods have seen limited adoption due to their inability to account for environmental uncertainty and operational constraints. In this work, we demonstrate that…
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Underwater glider robots have become indispensable for ocean sampling, yet fully autonomous long-term operation remains rare in practice. Although stakeholders are calling for tools to manage increasingly large fleets of gliders, existing methods have seen limited adoption due to their inability to account for environmental uncertainty and operational constraints. In this work, we demonstrate that uncertainty-aware online navigation planning can be deployed in real-world glider missions at scale. We formulate the problem as a stochastic shortest-path Markov Decision Process and propose a sample-based online planner based on Monte Carlo Tree Search. Samples are generated by a physics-informed simulator calibrated on real-world glider data that captures uncertain execution of controls and ocean current forecasts while remaining computationally tractable. Our methodology is integrated into an autonomous system for Slocum gliders that performs closed-loop replanning at each surfacing. The system was validated in two North Sea deployments totalling approximately 3 months and 1000 km, representing the longest fully autonomous glider campaigns in the literature to date. Results demonstrate improvements of up to 9.88% in dive duration and 16.51% in path length compared to standard straight-to-goal navigation, including a statistically significant path length reduction of 9.55% in a field deployment.
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Submitted 15 April, 2026; v1 submitted 22 February, 2026;
originally announced February 2026.
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New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0
Authors:
Steven B. Roberts,
Mustafa Ağgül,
Daniel R. Reynolds,
Cody J. Balos,
David J. Gardner,
Carol S. Woodward
Abstract:
SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements and new features added over the last three years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge-Kutta, s…
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SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements and new features added over the last three years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge-Kutta, symplectic partitioned Runge-Kutta, and operator splitting. In addition, we describe new time step adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge-Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.
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Submitted 9 February, 2026; v1 submitted 17 June, 2025;
originally announced June 2025.
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SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems
Authors:
Cody J. Balos,
Marc Day,
Lucas Esclapez,
Anne M. Felden,
David J. Gardner,
Malik Hassanaly,
Daniel R. Reynolds,
Jon Rood,
Jean M. Sexton,
Nicholas T. Wimer,
Carol S. Woodward
Abstract:
Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach…
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Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger "outer-loop" time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.
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Submitted 2 May, 2024;
originally announced May 2024.
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SpaCE: The Spatial Confounding Environment
Authors:
Mauricio Tec,
Ana Trisovic,
Michelle Audirac,
Sophie Woodward,
Jie Kate Hu,
Naeem Khoshnevis,
Francesca Dominici
Abstract:
Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating caus…
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Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.
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Submitted 3 December, 2024; v1 submitted 1 December, 2023;
originally announced December 2023.
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Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks
Authors:
John J. Loffeld,
Andy Nonaka,
Daniel R. Reynolds,
David J. Gardner,
Carol S. Woodward
Abstract:
Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever increasing size and complexity. Recently, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales,…
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Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever increasing size and complexity. Recently, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using IMEX and low-order operator splitting schemes. However, there have been few performance studies that compare different classes of multirate integrators on complex application problems. We study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits the work of Emmet et al. (2014) on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but run at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed implicit-explicit MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.
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Submitted 6 November, 2022;
originally announced November 2022.
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ARKODE: a flexible IVP solver infrastructure for one-step methods
Authors:
Daniel R. Reynolds,
David J. Gardner,
Carol S. Woodward,
Rujeko Chinomona
Abstract:
We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE also supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge--Kutta methods and multirate infi…
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We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE also supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge--Kutta methods and multirate infinitesimal (MRI) methods. We present the role of ARKODE within the SUNDIALS suite of time integration and nonlinear solver libraries, the core ARKODE infrastructure for utilities common to large classes of one-step methods, as well as its use of ``time stepper'' modules enabling easy incorporation of novel algorithms into the library. Numerical results show example problems of increasing complexity, highlighting the algorithmic flexibility afforded through this infrastructure, and include a larger multiphysics application leveraging multiple algorithmic features from ARKODE and SUNDIALS.
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Submitted 21 December, 2022; v1 submitted 27 May, 2022;
originally announced May 2022.
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Discrete, recurrent, and scalable patterns in human judgement underlie affective picture ratings
Authors:
Emanuel A. Azcona,
Byoung-Woo Kim,
Nicole L. Vike,
Sumra Bari,
Shamal Lalvani,
Leandros Stefanopoulos,
Sean Woodward,
Martin Block,
Aggelos K. Katsaggelos,
Hans C. Breiter
Abstract:
Operant keypress tasks, where each action has a consequence, have been analogized to the construct of "wanting" and produce lawful relationships in humans that quantify preferences for approach and avoidance behavior. It is unknown if rating tasks without an operant framework, which can be analogized to "liking", show similar lawful relationships. We studied three independent cohorts of participan…
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Operant keypress tasks, where each action has a consequence, have been analogized to the construct of "wanting" and produce lawful relationships in humans that quantify preferences for approach and avoidance behavior. It is unknown if rating tasks without an operant framework, which can be analogized to "liking", show similar lawful relationships. We studied three independent cohorts of participants (N = 501, 506, and 4,019 participants) collected by two distinct organizations, using the same 7-point Likert scale to rate negative to positive preferences for pictures from the International Affective Picture Set. Picture ratings without an operant framework produced similar value functions, limit functions, and trade-off functions to those reported in the literature for operant keypress tasks, all with goodness of fits above 0.75. These value, limit, and trade-off functions were discrete in their mathematical formulation, recurrent across all three independent cohorts, and demonstrated scaling between individual and group curves. In all three experiments, the computation of loss aversion showed 95% confidence intervals below the value of 2, arguing against a strong overweighting of losses relative to gains, as has previously been reported for keypress tasks or games of chance with calibrated uncertainty. Graphed features from the three cohorts were similar and argue that preference assessments meet three of four criteria for lawfulness, providing a simple, short, and low-cost method for the quantitative assessment of preference without forced choice decisions, games of chance, or operant keypressing. This approach can easily be implemented on any digital device with a screen (e.g., cellphones).
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Submitted 12 March, 2022;
originally announced March 2022.
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Enabling GPU Accelerated Computing in the SUNDIALS Time Integration Library
Authors:
Cody J. Balos,
David J. Gardner,
Carol S. Woodward,
Daniel R. Reynolds
Abstract:
As part of the Exascale Computing Project (ECP), a recent focus of development efforts for the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been to enable GPU-accelerated time integration in scientific applications at extreme scales. This effort has resulted in several new GPU-enabled implementations of core SUNDIALS data structures, support for programming paradig…
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As part of the Exascale Computing Project (ECP), a recent focus of development efforts for the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been to enable GPU-accelerated time integration in scientific applications at extreme scales. This effort has resulted in several new GPU-enabled implementations of core SUNDIALS data structures, support for programming paradigms which are aware of the heterogeneous architectures, and the introduction of utilities to provide new points of flexibility. In this paper, we discuss our considerations, both internal and external, when designing these new features and present the features themselves. We also present performance results for several of the features on the Summit supercomputer and early access hardware for the Frontier supercomputer, which demonstrate negligible performance overhead resulting from the additional infrastructure and significant speedups when using both NVIDIA and AMD GPUs.
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Submitted 8 December, 2021; v1 submitted 25 November, 2020;
originally announced November 2020.
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Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers
Authors:
David J. Gardner,
Daniel R. Reynolds,
Carol S. Woodward,
Cody J. Balos
Abstract:
In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers an…
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In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed "behind-the-scenes," with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.
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Submitted 22 September, 2021; v1 submitted 19 November, 2020;
originally announced November 2020.
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SUNDIALS Multiphysics+MPIManyVector Performance Testing
Authors:
Daniel R. Reynolds,
David J. Gardner,
Cody J. Balos,
Carol S. Woodward
Abstract:
In this report we document performance test results on a SUNDIALS-based multiphysics demonstration application. We aim to assess the large-scale parallel performance of new capabilities that have been added to the SUNDIALS suite of time integrators and nonlinear solvers in recent years under funding from both the Exascale Computing Project (ECP) and the Scientific Discovery through Advanced Scient…
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In this report we document performance test results on a SUNDIALS-based multiphysics demonstration application. We aim to assess the large-scale parallel performance of new capabilities that have been added to the SUNDIALS suite of time integrators and nonlinear solvers in recent years under funding from both the Exascale Computing Project (ECP) and the Scientific Discovery through Advanced Scientific (SciDAC) program, specifically: (a) SUNDIALS' new MPIManyVector module, that allows extreme flexibility in how a solution "vector" is staged on computational resources, (b) ARKode's new multirate integration module, MRIStep, allowing high-order accurate calculations that subcycle "fast" processes within "slow" ones, (c) SUNDIALS' new flexible linear solver interfaces, that allow streamlined specification of problem-specific linear solvers, and (d) SUNDIALS' new N_Vector additions of "fused" vector operations (to increase arithmetic intensity) and separation of reduction operations into "local" and "global" versions (to reduce latency by combining multiple reductions into a single MPI_Allreduce call). We anticipate that subsequent reports will extend this work to investigate a variety of other new features, including SUNDIALS' generic SUNNonlinearSolver interface and accelerator-enabled N_Vector modules, and upcoming MRIStep extensions to support custom "fast" integrators (that leverage problem structure) and IMEX integration of the "slow" time scale (to add diffusion).
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Submitted 27 September, 2019;
originally announced September 2019.
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Research and Education in Computational Science and Engineering
Authors:
Ulrich Rüde,
Karen Willcox,
Lois Curfman McInnes,
Hans De Sterck,
George Biros,
Hans Bungartz,
James Corones,
Evin Cramer,
James Crowley,
Omar Ghattas,
Max Gunzburger,
Michael Hanke,
Robert Harrison,
Michael Heroux,
Jan Hesthaven,
Peter Jimack,
Chris Johnson,
Kirk E. Jordan,
David E. Keyes,
Rolf Krause,
Vipin Kumar,
Stefan Mayer,
Juan Meza,
Knut Martin Mørken,
J. Tinsley Oden
, et al. (8 additional authors not shown)
Abstract:
Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that…
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Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.
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Submitted 31 December, 2017; v1 submitted 8 October, 2016;
originally announced October 2016.