update question mark

Author: Anthony David Gruber

_pages/about.md

@@ -47,6 +47,12 @@ Broad research keywords which tend to interest me include: scientific machine le
 
 Structure-Informed Model Reduction and Function Approximation
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+### Tensor Parametric Hamiltonian Operator Inference  [Preprint](https://arxiv.org/abs/2502.10888#){: .btn .btn--info .btn--small}{: .align-right}
+<img src="/images/tensor_wave.pdf" style="max-height: 300px; max-width: 300px; margin-right: 16px; margin-bottom: 10px" align=left>  **Abstract:** TThis work presents a tensor-based approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints, a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave speed.
+<br><br>
+(Joint with [Arjun Vijaywargia](https://arjunveejay.notion.site/Arjun-Vijaywargiya-4f155526b32e4b0a97b7f5dad4c89dde) and [Shane A. McQuarrie](https://github.com/shanemcq18).)
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 <img src="/images/GCNN_recon2.png" style="max-height: 275px; max-width: 325px; margin-right: 16px" align=left>  Due to their high computational cost, scientific studies based on large-scale simulation frequently operate at a data deficit which creates problems inverse to the issues with "big data".  Particularly, there is a need for efficient function approximation and model reduction strategies which can serve as cheap and reliable surrogates for the high-fidelity models used in practical applications.  These projects develop such technology using invariances and other structural considerations as a starting point, allowing for informed surrogates with beneficial behavior.
 
 <details markdown="1"><summary><b>Projects</b></summary>

_pages/talks.md

@@ -17,7 +17,7 @@ Some recorded presentations, current through 3/2025.
 - **Anthony Gruber**, NA-G-ROMs seminar series, ARIA project, INRIA, Bordeaux,
 FR. *Property-preserving model reduction for conservative and dissipative systems*, (50 min; Oct. 10, 2023).
 
-[Video](https://www.youtube.com/watch?v=k-XQqkfPPdc){: .btn .btn--info .btn--small}{: .align-right}
+[Video](https://www.youtube.com/watch?v=0alQZzR09nM){: .btn .btn--info .btn--small}{: .align-right}
 - **Anthony Gruber**, CRUNCH webinar (virtual), Brown University, Providence, RI. *Energetically consistent model reduction for Hamiltonian and metriplectic systems*, (50 min; Dec. 9, 2022).