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Volume 22, Issue 1
From Obstacle Problems to Neural Insights: Feedforward Neural Network Modeling of Ice Thickness

Kapil Chawla, William Holmes & Roger Temam

DOI: 10.4208/ijnam2025-1001

Int. J. Numer. Anal. Mod., 22 (2025), pp. 1-20.

Published online: 2024-11

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  • Abstract

In this study, we integrate the established obstacle problem formulation from ice sheet modeling [1, 2] with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By harmonizing the mathematical structure with an energy minimization framework tailored for neural network approximations, our method’s efficacy is confirmed through both 1D and 2D numerical simulations. Utilizing the NSIDC-0092 dataset for Greenland [22] and incorporating bedrock topography for model pre-training, we register notable advances in prediction accuracy. Our research underscores the potent combination of traditional mathematical models and advanced computational techniques in delivering precise ice thickness estimations.

  • Keywords

Neural networks, ice thickness estimation, obstacle problems, feedforward neural networks, mathematical modeling, partial differential equations.

  • AMS Subject Headings

68T01, 35R35, 65N99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-22-1, author = {Chawla , KapilHolmes , William and Temam , Roger}, title = {From Obstacle Problems to Neural Insights: Feedforward Neural Network Modeling of Ice Thickness}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {22}, number = {1}, pages = {1--20}, abstract = {

In this study, we integrate the established obstacle problem formulation from ice sheet modeling [1, 2] with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By harmonizing the mathematical structure with an energy minimization framework tailored for neural network approximations, our method’s efficacy is confirmed through both 1D and 2D numerical simulations. Utilizing the NSIDC-0092 dataset for Greenland [22] and incorporating bedrock topography for model pre-training, we register notable advances in prediction accuracy. Our research underscores the potent combination of traditional mathematical models and advanced computational techniques in delivering precise ice thickness estimations.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1001}, url = {http://global-sci.org/intro/article_detail/ijnam/23564.html} }
TY - JOUR T1 - From Obstacle Problems to Neural Insights: Feedforward Neural Network Modeling of Ice Thickness AU - Chawla , Kapil AU - Holmes , William AU - Temam , Roger JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 20 PY - 2024 DA - 2024/11 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1001 UR - https://global-sci.org/intro/article_detail/ijnam/23564.html KW - Neural networks, ice thickness estimation, obstacle problems, feedforward neural networks, mathematical modeling, partial differential equations. AB -

In this study, we integrate the established obstacle problem formulation from ice sheet modeling [1, 2] with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By harmonizing the mathematical structure with an energy minimization framework tailored for neural network approximations, our method’s efficacy is confirmed through both 1D and 2D numerical simulations. Utilizing the NSIDC-0092 dataset for Greenland [22] and incorporating bedrock topography for model pre-training, we register notable advances in prediction accuracy. Our research underscores the potent combination of traditional mathematical models and advanced computational techniques in delivering precise ice thickness estimations.

Chawla , KapilHolmes , William and Temam , Roger. (2024). From Obstacle Problems to Neural Insights: Feedforward Neural Network Modeling of Ice Thickness. International Journal of Numerical Analysis and Modeling. 22 (1). 1-20. doi:10.4208/ijnam2025-1001
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