Vikas Dwivedi

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Dr. Vikas
Dwivedi

Postdoctoral Researcher / CREATIS, INSA Lyon

Scientific machine learning and physics-informed AI for computational science and biomedical imaging.

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Portrait of Dr. Vikas Dwivedi
Vikas Dwivedi CREATIS · INSA Lyon

01 / About

About me

I am a Postdoctoral Researcher at CREATIS Biomedical Imaging Laboratory, INSA Lyon, France, working on scientific machine learning for forward and inverse PDE problems, with applications in computational fluid dynamics and medical imaging.

I completed my M.Tech at IIT Delhi and Ph.D. at IIT Madras under the supervision of Prof. Balaji Srinivasan. My background includes over two years in industry as a Data Scientist at Vunet Systems and almost three years of postdoctoral research in India, the United States, and France.

I received the Best PhD Thesis Award in Data Science from IIT Madras.

02 / Research

Research interests

Fast physics-informed PDE solvers

Development of fast, interpretable PDE solvers using shallow physics-informed learning machines and curriculum learning.

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Research focuses on developing computationally alternatives to deep Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs). Physics-Informed Extreme Learning Machines (PIELMs) were introduced, which employ shallow neural networks and replace iterative gradient-based training with a linear least-squares solve for linear PDEs. More recently, this framework was extended to nonlinear PDEs through curriculum learning, progressively solving a sequence of linearized problems of increasing complexity. These methods provide efficient and interpretable approaches to scientific computing, with applications including Burgers’ equation, incompressible Navier–Stokes flows, and hemodynamics.

Relevant papers: Dwivedi & Srinivasan (2020); Dwivedi et al. (2025).

Sharp gradients and domain decomposition

Development of localized neural methods for resolving sharp gradients and boundary layers in PDE solutions.

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Standard PINNs often struggle with localized features such as sharp gradients, boundary layers, and heterogeneous solution structures. To address the representational burden of global neural networks, Distributed Learning Machines (DLMs) were developed, which partition the computational domain into smaller regions represented by localized neural networks coupled through physics-based interface constraints. Building on the broader idea of localized representations, Gated X-TFC was subsequently developed, which employs differentiable gating functions to adapt radial basis function widths near sharp gradients without introducing explicit interface penalties. This approach preserves exact boundary-condition enforcement while improving accuracy and computational efficiency for challenging boundary-layer problems.

Relevant papers: Dwivedi et al. (2021); Dwivedi et al. (2026), Gated X-TFC.

Interpretable neural representations

Investigation of interpretable neural basis functions that adapt to the physics of parametric PDEs.

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Understanding how neural networks represent PDE solutions is an important research direction. Meta-SPINN was developed as a physics-informed meta-learning framework that learns how the underlying basis representation changes with the physical parameters of a PDE. Unlike conventional neural representations with largely implicit internal features, Meta-SPINN employs interpretable radial basis functions whose centers, scales, orientations, and coefficients adapt to the governing physics. This allows the learned representations to reveal meaningful solution structures, including transport trajectories, diffusion patterns, and shock fronts, while enabling predictions across families of parametric PDEs.

Relevant papers: Dwivedi et al. (2026), Meta-SPINN.

Compact neural representations

Reduction of geometric complexity in physics-informed models while maintaining approximation accuracy.

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A central question in physics-informed learning is how much representational complexity is actually required to approximate a PDE solution accurately. To investigate this, Kernel-Adaptive Physics-Informed Learning Machines (KAPI-LMs) were developed, which organize a large dictionary of radial basis functions using a smaller set of shared geometric parameters while retaining independent expansion coefficients. This framework introduces compressed variants of SPINN and PIELM, enabling substantial reductions in geometric complexity without necessarily reducing the number of physical basis functions. By controlling geometric sharing and adapting local resolution where necessary, KAPI-LMs provide a systematic approach to studying the relationship between representation complexity, approximation accuracy, and underlying physical structure.

Relevant papers: Dwivedi et al. (2026), KAPI-LM.

Physics-informed computer vision

Development of label-free, physics-informed methods for medical image segmentation.

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Another research direction is the application of physics-informed learning to computer vision, particularly medical image segmentation. Physics-Informed Contour Selection (PICS) was developed, a label-free segmentation framework that combines classical active contour models with physics-informed optimization. By representing contours using cubic splines and directly minimizing energy-based loss functions, PICS provides an interpretable and computationally lightweight alternative to conventional deep segmentation networks. The framework supports shape-based physical constraints and has been demonstrated for three-dimensional cardiac image segmentation, including left-ventricular segmentation.

Relevant papers: Dwivedi et al. (2024).

03 / Publications

Publications

Journal articles

  1. V. Dwivedi, B. Srinivasan, M. Sigovan, B. Sixou (2026). KAPI-LM: Kernel-Adaptive Physics-Informed Learning Machines for PDEs. Neural Networks, 206, 109740.

    DOI
    BibTeX
    @article{dwivedi2026kapilm,
  title = {KAPI-LM: Kernel-Adaptive Physics-Informed Learning Machines for PDEs},
  author = {V. Dwivedi and B. Srinivasan and M. Sigovan and B. Sixou},
  year = {2026},
  note = {Neural Networks, 206, 109740},
  doi = {10.1016/j.neunet.2026.109740}
}

  2. V. Dwivedi, M. Sigovan, B. Sixou (2026). Meta-SPINN: Meta-learned basis adaptation for parametric PDEs. Machine Learning: Science and Technology, 7(4), 045060.

    DOI
    BibTeX
    @article{dwivedi2026metaspinn,
  title = {Meta-SPINN: Meta-learned basis adaptation for parametric PDEs},
  author = {V. Dwivedi and M. Sigovan and B. Sixou},
  year = {2026},
  note = {Machine Learning: Science and Technology, 7(4), 045060},
  doi = {10.1088/2632-2153/ae94e2}
}

  3. V. Dwivedi, E. Schiassi, B. Sixou, M. Sigovan (2026). Gated X-TFC: Soft domain decomposition for forward and inverse problems in sharp-gradient PDEs. Neurocomputing, 676, 133090.

    DOI
    BibTeX
    @article{dwivedi2026gated,
  title = {Gated X-TFC: Soft domain decomposition for forward and inverse problems in sharp-gradient PDEs},
  author = {V. Dwivedi and E. Schiassi and B. Sixou and M. Sigovan},
  year = {2026},
  note = {Neurocomputing, 676, 133090},
  doi = {10.1016/j.neucom.2026.133090}
}

  4. V. Dwivedi, B. Sixou, M. Sigovan (2025). Curriculum learning-driven PIELMs for fluid flow simulations. Neurocomputing, 650, 130924.

    DOI
    BibTeX
    @article{dwivedi2025curriculum,
  title = {Curriculum learning-driven PIELMs for fluid flow simulations},
  author = {V. Dwivedi and B. Sixou and M. Sigovan},
  year = {2025},
  note = {Neurocomputing, 650, 130924},
  doi = {10.1016/j.neucom.2025.130924}
}

  5. V. Dwivedi, B. Srinivasan, G. Krishnamurthi (2024). Physics informed contour selection for rapid image segmentation. Scientific Reports, 14(1), 6996.

    DOI
    BibTeX
    @article{dwivedi2024physics,
  title = {Physics informed contour selection for rapid image segmentation},
  author = {V. Dwivedi and B. Srinivasan and G. Krishnamurthi},
  year = {2024},
  note = {Scientific Reports, 14(1), 6996},
  doi = {10.1038/s41598-024-57281-x}
}

  6. V. Dwivedi, B. Srinivasan (2022). A normal equation-based extreme learning machine for solving linear partial differential equations. Journal of Computing and Information Science in Engineering, 22(1), 014502.

    DOI
    BibTeX
    @article{dwivedi2022a,
  title = {A normal equation-based extreme learning machine for solving linear partial differential equations},
  author = {V. Dwivedi and B. Srinivasan},
  year = {2022},
  note = {Journal of Computing and Information Science in Engineering, 22(1), 014502},
  doi = {10.1115/1.4051530}
}

  7. V. Dwivedi, N. Parashar, B. Srinivasan (2021). Distributed learning machines for solving forward and inverse problems in partial differential equations. Neurocomputing, 420, 299–316.

    DOI
    BibTeX
    @article{dwivedi2021distributed,
  title = {Distributed learning machines for solving forward and inverse problems in partial differential equations},
  author = {V. Dwivedi and N. Parashar and B. Srinivasan},
  year = {2021},
  note = {Neurocomputing, 420, 299–316},
  doi = {10.1016/j.neucom.2020.09.006}
}

  8. V. Dwivedi, B. Srinivasan (2020). Solution of biharmonic equation in complicated geometries with physics informed extreme learning machine. Journal of Computing and Information Science in Engineering, 20(6), 061004.

    DOI
    BibTeX
    @article{dwivedi2020solution,
  title = {Solution of biharmonic equation in complicated geometries with physics informed extreme learning machine},
  author = {V. Dwivedi and B. Srinivasan},
  year = {2020},
  note = {Journal of Computing and Information Science in Engineering, 20(6), 061004},
  doi = {10.1115/1.4046892}
}

  9. V. Dwivedi, B. Srinivasan (2020). Physics informed extreme learning machine (PIELM) — a rapid method for the numerical solution of partial differential equations. Neurocomputing, 391, 96–118.

    DOI
    BibTeX
    @article{dwivedi2020physics,
  title = {Physics informed extreme learning machine (PIELM) — a rapid method for the numerical solution of partial differential equations},
  author = {V. Dwivedi and B. Srinivasan},
  year = {2020},
  note = {Neurocomputing, 391, 96–118},
  doi = {10.1016/j.neucom.2019.12.099}
}

  10. V. Dwivedi, B. Srinivasan (2018). Prediction of transition in temporal mixing layer using ILES. International Journal of Advances in Engineering Sciences and Applied Mathematics.

    DOI
    BibTeX
    @article{dwivedi2018prediction,
  title = {Prediction of transition in temporal mixing layer using ILES},
  author = {V. Dwivedi and B. Srinivasan},
  year = {2018},
  note = {International Journal of Advances in Engineering Sciences and Applied Mathematics},
  doi = {10.1007/s12572-018-0218-9}
}

Conference papers

  1. A. G. Srinivasan, V. Dwivedi, B. Srinivasan (2025). Towards Sustainable Scientific Machine Learning: Fast and interpretable PDE Solvers via RBF-PIELM. Proceedings of the 13th ACM IKDD International Conference on Data Science (CODS ’25), pp. 376–386.

    DOI
    BibTeX
    @inproceedings{srinivasan2025towards,
  title = {Towards Sustainable Scientific Machine Learning: Fast and interpretable PDE Solvers via RBF-PIELM},
  author = {A. G. Srinivasan and V. Dwivedi and B. Srinivasan},
  year = {2025},
  note = {Proceedings of the 13th ACM IKDD International Conference on Data Science (CODS ’25), pp. 376–386},
  doi = {10.1145/3799830.3799865}
}

  2. V. Dwivedi (2024). Global Versus Local: Evaluating AlexNet Architectures for Tropical Cyclone Intensity Estimation. International Conference on Pattern Recognition, pp. 409–423.

    DOI
    BibTeX
    @inproceedings{dwivedi2024global,
  title = {Global Versus Local: Evaluating AlexNet Architectures for Tropical Cyclone Intensity Estimation},
  author = {V. Dwivedi},
  year = {2024},
  note = {International Conference on Pattern Recognition, pp. 409–423},
  doi = {10.1007/978-3-031-78186-5_27}
}

Workshop papers

  1. A. Daniel, V. Dwivedi, B. Srinivasan (2026). AB-PIELMs: Adaptive-basis physics-informed extreme learning machines for residual-driven domain decomposition. AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.

    PDF ↗
    BibTeX
    @inproceedings{daniel2026abpielms,
  title = {AB-PIELMs: Adaptive-basis physics-informed extreme learning machines for residual-driven domain decomposition},
  author = {A. Daniel and V. Dwivedi and B. Srinivasan},
  year = {2026},
  booktitle = {AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations},
  url = {https://openreview.net/pdf?id=QWbki1SyWm}
}

  2. V. Dwivedi, M. Sigovan, B. Sixou (2026). Kernel-Adaptive Physics-Informed Shallow Meta-Learning for Parametric Linear PDEs. AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.

    PDF
    BibTeX
    @inproceedings{dwivedi2026kerneladaptive,
  title = {Kernel-Adaptive Physics-Informed Shallow Meta-Learning for Parametric Linear PDEs},
  author = {V. Dwivedi and M. Sigovan and B. Sixou},
  year = {2026},
  booktitle = {AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations},
  url = {https://openreview.net/pdf?id=YyTEEVEVid}
}

  3. A. G. Srinivasan, V. Dwivedi, B. Srinivasan (2025). Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation. NeurIPS 2025 Workshop on Machine Learning and the Physical Sciences (ML4PS).

    PDF
    BibTeX
    @inproceedings{srinivasan2025deepvsshallow,
  title = {Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation},
  author = {Srinivasan, Akshay Govind and Dwivedi, Vikas and Srinivasan, Balaji},
  year = {2025},
  booktitle = {Machine Learning and the Physical Sciences Workshop (ML4PS), NeurIPS 2025},
  url = {https://ml4physicalsciences.github.io/2025/files/NeurIPS_ML4PS_2025_328.pdf}
}

  4. V. Dwivedi, M. Sigovan, S. Bruno (2025). Curriculum-Learning PIELMs for Hemodynamic Flows. OPT 2025: Optimization for Machine Learning.

    PDF
    BibTeX
    @inproceedings{dwivedi2025curriculumlearning,
  title = {Curriculum-Learning PIELMs for Hemodynamic Flows},
  author = {V. Dwivedi and M. Sigovan and S. Bruno},
  year = {2025},
  note = {OPT 2025: Optimization for Machine Learning},
  url = {https://www.opt-ml.org/papers/2025/paper11.pdf}
}

  5. V. Dwivedi, M. Sigovan, S. Bruno (2025). Empirical-Bayes XTFC for Inverse Parameter Estimation. OPT 2025: Optimization for Machine Learning.

    PDF
    BibTeX
    @inproceedings{dwivedi2025empiricalbayes,
  title = {Empirical-Bayes XTFC for Inverse Parameter Estimation},
  author = {V. Dwivedi and M. Sigovan and S. Bruno},
  year = {2025},
  note = {OPT 2025: Optimization for Machine Learning},
  url = {https://www.opt-ml.org/papers/2025/paper150.pdf}
}

For most updated research, see my Google Scholar profile ↗.