I am an AI Researcher with a background in pure and applied mathematics, scientific computing, and machine learning. My research develops mathematically grounded methods for scientific AI, representation learning, operator learning, and foundation models, with applications ranging from atmospheric dynamics and data assimilation to biomedical AI.
My work bridges theory and practice through:
- Mathematical foundations of AI and representation learning
- Scientific machine learning and neural operators
- Koopman and kernel operator methods
- Sparse and efficient neural architectures
- Generative and foundation models for physical systems
- Mechanistic interpretability and representation dynamics
- Scientific Foundation Models — generative modeling, uncertainty, and ensemble learning for physical systems
- Representation Learning — geometry, invariance, kernels, and operator-adapted representations
- Operator Learning — Koopman operators, neural operators, and spectral methods
- Efficient AI — sparse neural networks, compact-support kernels, and structured architectures
- Mechanistic Interpretability — representation dynamics and internal mechanisms of language models
- AI for Science & Medicine — atmospheric science, data assimilation, and biomedical learning
Himanshu Singh, Steven J. Greybush, Laura E. Dailey, Melissa Adrian, and Romit Maulik
40th Conference on Neural Information Processing Systems (NeurIPS 2026)
A matrix-free framework for learning and evaluating covariance response in generative weather ensembles, motivated by the requirements of ensemble-based data assimilation.
Himanshu Singh
40th Conference on Neural Information Processing Systems (NeurIPS 2026)
Develops an inverse geometric formulation of representation learning: rather than modifying an operator to preserve a prescribed geometry, construct an RKHS geometry in which the given operator acts isometrically. The work characterizes the complete family of admissible invariant kernels and develops operator-adapted Gaussian representations.
📄 Paper · 🌐 Interactive Project Website · 💻 Code
Kernelized Koopman Representation Geometry Governs Transient Amplification in Neural Dynamical Systems
Himanshu Singh
NeurIPS 2026 Workshop on Symmetry and Geometry in Neural Representations — Proceedings Track
Studies how kernel-induced representation geometry governs transient amplification in neural dynamical systems through a Koopman-operator perspective.
📄 Paper · 🌐 Interactive Project Website · 💻 Project Repository
Which Anatomy Matters Under Limited Labels? A Data-Efficient Anatomy-Aware Benchmark for Cardiac Pathology Prediction
Himanshu Singh
43rd International Conference on Machine Learning (ICML 2026), Seoul, South Korea — PMLR 306
Investigates low-data cardiac pathology prediction using anatomy-aware representations, asking whether carefully chosen anatomical structure can provide more useful predictive information than increased model complexity.
Himanshu Singh and Drishty Singh
International Conference on Scientific Computing and Machine Learning (SCML 2026)
Introduces a sparse Koopman neural-operator framework for atmospheric dynamics, combining latent-space evolution, spectral stability, and scalable scientific machine learning.
📄 Paper · 💻 Project Repository
Himanshu Singh
AI4X – Accelerate, Singapore, 16–19 June 2026
Develops compact-support graph kernels as a sparse alternative to dense global pairwise mixing, using localized kernel structure to reduce interaction complexity while retaining global representation capability.
Nishant Panda, Himanshu Singh, and J. Nathan Kutz
arXiv:2505.06806, 2025
Studies the operator-theoretic foundations of kernel Dynamic Mode Decomposition by constructing a Laplacian-kernel RKHS and investigating closability of Koopman operators, with applications to sparse spatiotemporal reconstruction.
Machine Learning Application of Generalized Gaussian Radial Basis Function and Its Reproducing Kernel Theory
Himanshu Singh
Mathematics, 12(6), 829, 2024
Develops the reproducing-kernel theory of the Generalized Gaussian Radial Basis Function and investigates its use in machine-learning architectures including kernel regression, support vector machines, and neural networks.
| Area | Topics |
|---|---|
| Scientific AI | Foundation models, generative ensembles, data assimilation |
| Operator Learning | Koopman operators, neural operators, FNO |
| Representation Learning | RKHS geometry, invariant representations, kernel methods |
| Efficient AI | Sparse neural networks, graph kernels, structured models |
| Mechanistic Interpretability | Representation dynamics, activation analysis, LLM behavior |
| Applied AI | Atmospheric science, biomedical imaging, dynamical systems |
- Atmospheric Foundation Models — generative ensemble modeling and data assimilation
- Operator-Adapted RKHS Geometry — structure-preserving representation learning
- Sparse Koopman Neural Operators — stable learning of atmospheric dynamics
- Kernel Koopman Theory — RKHS closability and sparse dynamical reconstruction
- Mechanistic Interpretability of LLMs — representation and repetition dynamics
- Anatomy-Aware Biomedical AI — data-efficient cardiac pathology prediction
Python · PyTorch · Scientific ML · Neural Operators · Koopman Operators · RKHS · Kernel Methods · Generative Models · Diffusion Models · Graph Neural Networks · High-Performance Computing
🌐 Personal Website · 💻 GitHub · 📄 Koopman–RKHS Project
Research theme: developing mathematically grounded and computationally scalable AI for learning representations, operators, and uncertainty in complex scientific systems.