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During my research at the Indian Institute of Science (IISc), Bengaluru, my team and I developed a new framework called Adaptive Multiscale Operator Correction (AMOC). Our work addresses a common problem in scientific machine learning: neural operators often struggle to capture high-frequency details and sharply localized features when solving partial differential equations (PDEs).
AMOC combines neural operator learning, including Fourier Neural Operators, with physics-constrained optimization in an adaptive spectral subspace built from Fourier and wavelet bases. This allows the model to correct errors in the regions and frequency ranges where standard neural operators tend to struggle. Across heat, Poisson, Darcy, and Helmholtz equations, our approach achieved error reductions of up to four orders of magnitude compared with standard baselines, particularly on out-of-distribution problems.
Our paper has been accepted at NeurIPS 2026, and we have released the code publicly. As the first author, I am seeking travel support to present our work in person at the conference in Sydney, Australia.
Paper link: https://neurips.cc/virtual/2026/loc/sydney/poster/149265
Project link: https://github.com/subhampatel2899/AMOC
My immediate goal is to present our accepted NeurIPS 2026 paper in Sydney and discuss our findings with researchers working in scientific machine learning, computational mathematics, and physics-informed AI. I want to learn from their feedback, particularly on the trade-offs between computational cost and accuracy, and on how to choose suitable spectral bases for different physical problems.
The broader goal of our research is to develop fast AI-based approximations for PDEs without losing important physical details. Neural operators can make predictions much faster than conventional numerical solvers, but they may smooth out sharp peaks, boundary layers, and other localized features that matter for accurate simulations. Through AMOC, we are exploring how adaptive Fourier and wavelet corrections can address this limitation while keeping the computational cost manageable.
At NeurIPS, I plan to present our method, discuss its strengths and limitations with other researchers, and gather feedback that can guide our next experiments. After the conference, I will bring these insights back to IISc to help us improve our hybrid Fourier-wavelet models, address memory limitations in three-dimensional wavelet representations, and explore residual-aware basis selection. These developments could support future applications in high-dimensional wave propagation and atmospheric dynamics.
I am requesting financial support to travel from Bengaluru to Sydney to present our accepted paper at NeurIPS 2026. As a Ph.D. scholar, covering the cost of international conference travel independently would be difficult.
My minimum funding request is $1,200, which would cover round-trip airfare. My full funding goal is $3,100, covering the estimated costs of attending the conference.
The estimated budget is:
Round-trip flights: $1,200
Accommodation: $1,000
Meals and incidentals: $450
Conference registration: $300
Local transportation and poster printing: $150
Total requested: $3,100
I am also exploring institutional travel support and external grants. However, I have not yet secured funding specifically for this trip. Any support received would help me attend and present the work in person.
Our research team works across the Department of Computational and Data Sciences and the Department of Mathematics at the Indian Institute of Science. The team consists of me, Subham Patelm Himanshu Pandey and our corresponding author and mentor, Dr. Ratikanta Behera.
As the first author of the accepted NeurIPS 2026 paper, I led several of the project's main technical contributions. These included formulating the Tikhonov-regularized least-squares wavelet projection, developing the AMOC architecture in PyTorch, running multi-GPU physics-informed optimization experiments, and deriving closed-form derivatives using Hermite polynomials.
My research focuses on scientific machine learning, computational mathematics, and neural operators for parametric PDEs. I have worked extensively with Fourier-based, wavelet-based, and physics-informed neural operator methods.
Our accepted NeurIPS paper and publicly available code reflect the team's ability to develop, test, and share computational research. I am now seeking support to present these results to the research community and use the feedback to guide our next stage of work.
Our research team works across the Department of Computational and Data Sciences and the Department of Mathematics at the Indian Institute of Science. The team consists of me, Subham Patel; Himanshu Pandey; and our corresponding author and mentor, Dr. Ratikanta Behera.
As the first author of the accepted NeurIPS 2026 paper, I led several of the project's main technical contributions. These included formulating the Tikhonov-regularized least-squares wavelet projection, developing the AMOC architecture in PyTorch, running multi-GPU physics-informed optimization experiments, and deriving closed-form derivatives using Hermite polynomials.
My research focuses on scientific machine learning, computational mathematics, and neural operators for parametric PDEs. I have worked extensively with Fourier-based, wavelet-based, and physics-informed neural operator methods. My previous research includes hybrid models for atmospheric dynamics, with work presented at TROPMET 2026, as well as theoretical stability bounds and convergence proofs for time-fractional equations.
Our accepted NeurIPS paper and publicly available code reflect the team's ability to develop, test, and share computational research. I am now seeking support to present these results to the research community and use the feedback to guide our next stage of work.
The research itself will continue even if I cannot travel. Our paper has been accepted, the methodology has been developed and evaluated, and the code is publicly available. The main risk is that I may be unable to attend NeurIPS in person because of the high cost of international travel from India.
Without travel support, I would miss the opportunity to present our findings directly to the conference community and discuss the work with researchers who could offer useful technical feedback or identify potential collaborations. These discussions would be particularly helpful as we work on the memory demands of three-dimensional wavelet representations and investigate better ways to select correction bases based on model errors.
Presenting at NeurIPS would also be an important step in my development as a researcher in scientific machine learning and computational mathematics. Funding would allow me to share the work in person, represent our research group at IISc, and bring new ideas back to our ongoing research. Without it, the paper and code would remain accessible, but these opportunities for direct engagement would be limited.
Our research team works across the Department of Computational and Data Sciences and the Department of Mathematics at the Indian Institute of Science. The team consists of me, Subham Patel; Himanshu Pandey; and our corresponding author and mentor, Dr. Ratikanta Behera.
As the first author of the accepted NeurIPS 2026 paper, I led several of the project's main technical contributions. These included formulating the Tikhonov-regularized least-squares wavelet projection, developing the AMOC architecture in PyTorch, running multi-GPU physics-informed optimization experiments, and deriving closed-form derivatives using Hermite polynomials.
My research focuses on scientific machine learning, computational mathematics, and neural operators for parametric PDEs. I have worked extensively with Fourier-based, wavelet-based, and physics-informed neural operator methods. My previous research includes hybrid models for atmospheric dynamics, with work presented at TROPMET 2026, as well as theoretical stability bounds and convergence proofs for time-fractional equations.
Our accepted NeurIPS paper and publicly available code reflect the team's ability to develop, test, and share computational research. I am now seeking support to present these results to the research community and use the feedback to guide our next stage of work.
The research itself will continue even if I cannot travel. Our paper has been accepted, the methodology has been developed and evaluated, and the code is publicly available. The main risk is that I may be unable to attend NeurIPS in person because of the high cost of international travel from India.
Without travel support, I would miss the opportunity to present our findings directly to the conference community and discuss the work with researchers who could offer useful technical feedback or identify potential collaborations. These discussions would be particularly helpful as we work on the memory demands of three-dimensional wavelet representations and investigate better ways to select correction bases based on model errors.
Presenting at NeurIPS would also be an important step in my development as a researcher in scientific machine learning and computational mathematics. Funding would allow me to share the work in person, represent our research group at IISc, and bring new ideas back to our ongoing research. Without it, the paper and code would remain accessible, but these opportunities for direct engagement would be limited.
My Ph.D. research is supported by a fellowship through the Axis Bank Centre for Mathematics and Computing at IISc and the Ministry of Education (MoE), Government of India. This support covers my regular academic stipend, but it does not cover the international travel expenses for this conference.
I have not raised any external funding specifically for my NeurIPS 2026 trip to Sydney, and no travel grants for this trip have been confirmed. I am actively exploring institutional assistance and other funding opportunities.
Support through this request would help bridge that gap and make it possible for me to present our accepted research in person at NeurIPS 2026.