Research

My research interests broadly lie at the intersection of fluid dynamics, data assimilation, and scientific machine learning (SciML). I am currently interested in improving our understanding and modeling of complex flow phenomena across engineering and geophysical systems, and thereby help develop robust prediction systems, eventually in the form of digital twins, with the help of SciML in this era of big data. My motivation is that, in the big-picture sense, whatever I do can even infinitesimally contribute toward helping humanity achieve the Sustainable Development Goals, particularly SDG 9 on industry and innovation, SDG 11 on safe and sustainable cities, and SDG 13 on urgent climate action. Although control is not my current expertise, I want to venture into it as well. After all, prediction and control go hand in hand, and ideally they need to be realized together.

My current research focus is on developing fast, accurate, and uncertainty-aware prediction frameworks using SciML for urban micrometeorology. Micrometeorology refers to meteorological phenomena from the Earth’s surface up to an altitude of about 100 meters, where the flow and thermal environment are strongly influenced by buildings, human activities, and many other local factors. For real-time prediction, it may be necessary, for example, to complete a 30-minute time integration within only a few minutes. Prediction of such micrometeorological phenomena in real time still cannot be achieved even with today’s highest-performance supercomputers. In Japan, Prof. Ryo Onishi’s research group has been undertaking pioneering efforts in this field, and that forms the immediate foundation of my present research direction. I also believe that the same research foundation can contribute to other meteorological problems, such as rainfall prediction, which is especially important in Japan. In particular, linear precipitation bands, called senjo-kousuitai in Japanese, pose serious problems for many human activities, including the operation of railway services.

Also, I think that, in this era of AI-powered discovery and prediction in science and engineering, it is not enough to provide only trust by performance, through accuracy, speed, and efficiency. It is equally important to build trust through understanding, by designing these ML-based frameworks to be more inherently interpretable, for example through autoencoder-based model-order reduction, and also by exploring the potential of explainable AI (XAI). What interests me is not only whether an ML-based prediction system performs well, but also whether we can understand, from the perspective of a fluid dynamics scientist/meteorologist, what physical structures the model is attributing importance to. This can help human experts intervene when needed, diagnose failures, and hopefully at least partly soften the curse of the black-box nature of AI. "Explainable AI: Learning from the Learners" is a recent paper by Vinuesa, Brunton and Mengaldo, that nicely discusses these aspects.  

This, at the very least, my vision for my near-future research goals.

Keywords: fluid dynamics, scientific machine learning (SciML), data assimilation, urban micro-meteorology, numerical weather prediction (NWP), turbulence, vortex dynamics, hydrodynamic stability, computational fluid dynamics (CFD), reduced-order modeling, data-driven modeling, uncertainty quantification.

Uncertainty-Aware Spatiotemporal Super-Resolution Data Assimilation with Diffusion Models

Data assimilation tries to recover the evolving state of a chaotic flow by combining a forecast model with sparse, noisy observations. In many geophysical problems, however, accurate probabilistic DA is very expensive because it usually requires repeated high-resolution forecasts and large ensembles. This raises a practical question: can we obtain high-resolution, uncertainty-aware analyses much more cheaply by learning from data?

In this work, we developed DiffSRDA, a diffusion-model-based spatiotemporal super-resolution data assimilation framework. The idea is to use a short sequence of low-resolution forecasts together with sparse observations to generate plausible high-resolution analysis windows, while also producing an ensemble that quantifies uncertainty. We tested the method on an idealized barotropic jet instability problem, where the flow undergoes meandering, vortex roll-up, filamentation, and chaotic evolution.

The main result is that DiffSRDA achieves reconstruction quality close to a high-resolution Ensemble Kalman Filter, despite relying only on low-cost low-resolution forecasts during cycling. The sampled ensemble also captures physically meaningful uncertainty, with spread concentrated in dynamically active regions. A key practical finding is that accurate DiffSRDA cycling does not require long reverse diffusion chains: most of the full-chain accuracy is retained with only a few reverse steps. We also showed that the score-based structure of diffusion sampling allows training-free observation-consistency guidance, so the same pretrained model can better adapt to changed sensor layouts without retraining. Overall, this work shows that diffusion models can provide a practical and uncertainty-aware route to data assimilation in chaotic fluid flows.

For more details, please refer to: Ayapilla, A.S.P., Miyashita, K., Yasuda, Y., Onishi, R. 2026 "Uncertainty-Aware Spatiotemporal Super-Resolution Data Assimilation with Diffusion Models" https://arxiv.org/abs/2604.21180. 

Code available at: https://github.com/Pranithhazard/DiffSRDA

PhD thesis: Theoretical and Numerical Studies on Triangular Instability of Strained Vortices in Incompressible Flows 

A vortex column subjected to elliptic stretching is known to become unstable to short-wavelength disturbances whose wavelength is much smaller than the vortex core. This is the well-known elliptic instability (Moore & Saffman, 1975; Tsai & Widnall, 1976), which appears, for example, in interacting vortex pairs such as airplane wingtip vortices that induce mutual elliptic strain. The mechanism is a parametric resonance of Kelvin waves: two intrinsic Kelvin modes of the vortex resonate with the imposed strain (acting as a third mode), leading to exponential growth of the disturbance. A related mechanism also appears in curvature instability (Hattori & Fukumoto, 2003; Fukumoto & Hattori, 2005), where the strain is generated by the vortex’s own curvature, as in vortex rings.

This naturally raises a broader question: if elliptic and curvature-induced strain can trigger Kelvin-wave resonance, can triangular straining do something similar? Earlier studies suggested yes, but evidence was limited to idealized Rankine vortices. In my PhD work, I investigated this question for smoother and more realistic vortex models, especially the Lamb-Oseen and Batchelor vortices, which are more representative of wake vortices in rotating machinery. This is particularly relevant for three-bladed rotors (such as wind turbines and propellers), where the surrounding tip vortices can plausibly impose a threefold-symmetric strain on the hub vortex, deforming it into a triangular shape and potentially exciting resonance between Kelvin waves whose azimuthal wavenumbers differ by three.

Using a combination of theoretical analysis and numerical simulations, I demonstrated that a Lamb–Oseen vortex under triangular straining is indeed unstable, establishing the existence and basic characteristics of what we call triangular instability in a smooth vortex model. A key difference from the Rankine-vortex picture is that, in Lamb–Oseen-type vortices, some Kelvin waves are affected by critical-layer damping, which significantly influences which resonant modes actually become unstable. I then extended the analysis to Batchelor vortices to examine the role of axial flow (a common feature in real wake vortices), and showed that even modest axial flow can strongly modify the dispersion curves, resonance conditions, and dominant unstable modes. I also carried out nonlinear simulations to explore how the instability evolves beyond the linear stage, including mode-dependent vortex deformation, partial breakdown, and relaminarization behavior (an ongoing part of the work). Overall, this study aims to improve our understanding of wake-vortex instability mechanisms and may be relevant to more accurate modeling and control of wind-turbine wakes.

For more details, refer to:
1) Ayapilla, A.S.P., Hattori, Y. & Le Dize`s, S. 2025 "Triangular instability of a strained Lamb-Oseen vortex" is published in vol 1016 of Journal of Fluid Mechanics.

2) Ayapilla, A.S.P., Hattori, Y. & Le Dize`s, S. 2026 "Triangular instability of a strained Batchelor vortex" is published in  Journal of Fluid Mechanics.

Master's thesis: Data-driven subgrid modeling in LES of forced two-dimensional (2-D) turbulence

Two-dimensional turbulence, also known as Kraichnan turbulence, plays a key role in understanding large-scale atmospheric and interstellar flows. The lack of a third dimension significantly alters the turbulent cascade compared to its 3-D counterpart. In 2-D turbulence, enstrophy exhibits a forward cascade, dissipating at small scales, while energy undergoes a reverse cascade, accumulating at larger scales. When forcing is applied at a specific wavenumber, it can lead to the formation of distinct coherent structures depending on the nature of the forcing.

We utilized shallow artificial neural networks to model subgrid vorticity transport directly from the filtered vorticity field and its gradients, differing from traditional subgrid models that rely on velocity fields. Our approach was tested in both a priori and a posteriori frameworks, achieving a stable LES with accurate statistics. This method also allowed us to track the neural networks’ predictions of enstrophy flux, a critical quantity in 2-D turbulence, while offering improved interpretability for model diagnostics and enhancements.

For more details, refer to: A. S. P. Ayapilla and Y. Hattori. A data-driven approach to model enstrophy transfers in large eddy simulation of forced two-dimensional turbulence. Phys. Fluids, 35(7) (2023). 

Code available at: https://github.com/Pranithhazard/2dturbulence_ann_sgs

Undergraduate project: Simulation of a high Reynolds number turbulent jet flow using Lattice Boltzmann Method (LBM)