Objectives

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To complete the project objectives, 6 steps are required: (1) Sparse Identification of Nonlinear Dynamics (SINDy) installation and testing via toy problems provided source code developers, (2) estimate derivatives, (3) build a library of candidate functions, (4) set up and apply the sparse regression problem, (5) interpret the identified model, and (6) validate model. Data for 316H SS and alloy 617 data will be provided by the project partner. The target deliverable is a journal publication in Journal of Nuclear Materials.

The deliverables defined by the project partner are the following. (Please note that these may need modifying based on course deliverables.)

• Team Charter/Working Agreement: Due early Fall term, with revisions as needed.
• Planning Document: Due early Fall term, with revisions as needed.
• Task Distribution Document: Due mid-Fall term, with revisions as needed.
• GitHub Repository Generation: Due mid-Fall term.
• Publication Progression Report: Due at the end of each term.
• GitHub Code Releases: Due at the end of each term.
• Project Presentations: Due once per term.
• Publication Manuscript Submission: Due at the end of Spring term.

Motivations

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Nuclear fuel, cladding, and structural material development have been essential in the process of optimizing functionality and safety during nuclear reactor operations. Complying with nuclear regulations, new material behavior under the specified conditions must be investigated to comprehend the short- and long-term performance. Although data from scientific literature, material databases, manufacturer data sheets, and technical standards are available, applicability for existing materials under new operating conditions is not guaranteed. For new materials and manufacturing methods, data availability can be lost and must be supplemented with new experimental data. To increase the volume of viable data, a method to test the relevance for a certain material property is desired. To identify, process, and assess similarity of material dynamic behavior, we hypothesize a data postprocessing framework that will extract governing equations, automate equation non-dimensionalization, and output governing equation similarity is required. The extraction of governing equations can be achieved by applying Sparse Identification of Nonlinear Dynamics (SINDy). As a proof of concept and the first attempt to assess the applicability of SINDy to material and manufacturing data, we propose to apply SINDy to 316H stainless steel (SS) and alloy 617 material test and manufacturing data. Provided with phenomenon relationships developed by state of art materials science, SINDy extracted governing equations will be compared. The results of the research will be the fundamental platform of the data postprocessing framework as future work will be on equation non-dimensionalization and similarity identification automation.

Qualifications

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Minimum Qualifications:

• Foundational Mathematics Knowledge: linear algebra, differential equations, basic probability/statistics.
• Basic Programming and Computational Skills: Python, SciPy, scikit-learn.
• Basic Dynamical Systems Knowledge: time series, signal processing, state-space representation.
• Communication and Interdisciplinary Collaboration: ability to interpret and explain discovered models, skills in documenting assumptions and uncertainties.
• Teamwork Experience: working with fellow students, coordinating with team members, scheduling and executing work plans.

Preferred Qualifications:

• Awareness of Sparse Identification of Nonlinear Dynamics (SINDy): knowing the importance derivative estimations, understanding in sparse regression, familiarity with library construction.
• Strong Computational Background: sparse regression algorithms, high performance computing (HPC), automatic differentiation, machine learning frameworks (PyTorch, TensorFlow).
• Practical Experience with Extensions of SINDy: knowledge of SINDy variants (e.g., SINDy-PI, SINDYc, PDE-FIND)
• Experience with model selection, validation, cross-validation strategies.

Details

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Project Partner:

Ramon Yoshiura

NDA/IPA:

No Agreement Required

Number Groups:

5

Project Status:

Accepting Applicants

Keywords:
Data ScienceSparse Identification of Nonlinear DynamicsMaterial TestingMaterial Manufacturing