Multiscale Neural Operators
Adaptive wavelet and spectral architectures designed to capture both global flow dynamics and fine localized structures.
PhD Scholar · Indian Institute of Science, Bengaluru
Subham Patel
Operator Learning, Machine Learning, Wavelets in Scientific Computing, Fractional Partial Differential Equations.
About
Biography
Mr. Subham Patel is a PhD scholar at the Indian Institute of Science (IISc), Bengaluru, in the Department of Mathematics and the Department of Computational and Data Sciences under the IISc Mathematics Initiative. He is pursuing his research under the guidance of Prof. Ratikanta Behera (Department of Computational and Data Sciences) and Prof. Thirupathi Gudi (Department of Mathematics).
His research lies at the intersection of operator learning, machine learning, wavelets in scientific computing and fractional partial differential equations. He is supported by the MoE and Axis Bank PhD Fellowship. He holds an Integrated M.Sc. in Mathematics with a minor in Electrical Engineering from the National Institute of Technology (NIT) Rourkela.
Position
PhD Scholar, IISc Mathematics Initiative
Department
Mathematics & CDS, Indian Institute of Science
Fellowship
MoE & Axis Bank PhD Fellowship
Prior degree
Integrated M.Sc. Mathematics, NIT Rourkela
Research
Research Interests
Multiscale operator learning, physics-guided refinement, and adaptive numerical schemes.
Physics-Guided Correction
Hybrid frameworks coupling data-driven neural operators with low-dimensional spectral subspace optimization for robust generalization.
Singular & Fractional Systems
High-order graded mesh discretizations and wavelet collocation schemes tailored for complex multi-singular and delay PDEs.
Publications
Research publications
Peer-reviewed work in operator learning, numerical analysis and scientific computing.
2026
Adaptive multiscale operator correction via learned spectral subspace and physics-informed optimization
Advances in Neural Information Processing Systems (NeurIPS), 2026 Published
2025
An efficient hybrid numerical approach for time-fractional sub-diffusion equations with multi-singularities
Numerical Algorithms (Springer) Published
Articles under review
Under review
An adaptive second-generation wavelet neural operator for multiscale parametric PDEs
arXiv preprint arXiv:2607.02715
Recognition
Awards & achievements
National-level examinations and competitive fellowships.
2023 – Present
MoE & Axis-IISc Ph.D. Fellowship
2022
GATE 2022 — Mathematics
2022
CSIR NET (LS) 2022 — Mathematics
2022
GATE 2022 — Statistics
Academics
Education
From an integrated mathematics degree with an electrical engineering minor to doctoral research at IISc.
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PhD in Mathematics
IISc Mathematics Initiative · Department of Mathematics
Advisor: Prof. Ratikanta Behera, Prof. Thirupathi Gudi
CPI: 8.20/10.
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Integrated M.Sc. in Mathematics
Department of Mathematics · National Institute of Technology Rourkela
Five-year integrated master's programme in mathematics.
CPI: 8.23/10.
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Minor: Electrical Engineering
Department of Electrical Engineering · National Institute of Technology Rourkela
Completed alongside the Integrated M.Sc. in Mathematics.
CPI: 8.24/10.
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Senior School Certificate (Class XII)
Higher secondary education in the science stream.
Percentage: 86.8%.
Outreach
Workshops & conferences
Feb 10–12, 2026
International Conference on Advanced Scientific Computing & Machine Learning
Apr 24–28, 2025
The Thirteenth International Conference on Learning Representations (ICLR)
Nov 28, 2024
Adobe–IISc Research Workshop
Dec 14–15, 2023
Workshop on Mathematics and Computing of Uncertainty Quantification in Model-Based Simulation for Risk-Informed Decision Making
Nov 17–18, 2023
Workshop on Tensor Computation and Machine Learning (TCML), IISc, Bengaluru
Contact
Get in touch
Open to discussions on wavelets, numerical analysis, scientific machine learning and collaboration.
Contact details
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Office Room CDS 226
Department of Computational and Data Sciences
Indian Institute of Science
Bengaluru, Karnataka 560012