arXiv subjects

Atiyo Ghosh

Publications and source records attributed to Atiyo Ghosh.

6 recordsLinked to original sources

arXiv2026

Ordered Diffusion Kernels

We introduce Ordered Diffusion Kernels (ODKs), a novel class of local kernels that can approximate the infinitesimal generator of an arbitrary It\^o Stochastic Differential Equation (SDE). ODKs are designed to be applied to data sampled from dynamical systems where little dynamical information is available a priori. The Laplacian of classical diffusion kernels approximates the Laplace-Beltrami operator on the underlying manifold; adjusting the normalisation introduces an advection term that depends on the sampling density; recently, TMDmap generalised this normalisation to target an arbitrary measure, but at the cost of coupling advection to diffusion. More general local kernels can learn arbitrary second-order elliptic operators but are formulated in terms of known velocity fields --- making the first step of any analysis a potentially ill-posed inference problem. To formulate ODK, we first relax the problem of potential estimation to the more tractable task of inferring an ordering of the data, which we represent through an ordering function. We prove ODK's Laplacian converges to the infinitesimal generator of a gradient-flow SDE with state-dependent isotropic diffusion, without coupling advection and diffusion. We provide various extensions of ODK to: arbitrary drifts via local ordering functions; anisotropic diffusions via a Strang splitting scheme; multiple ordering functions; and self-tuning bandwidths. In addition, we introduce two loss functions which exploit the structure of ODKs to solve a non-parametric inference problem. We validate this framework on synthetic data from deterministic and stochastic systems, demonstrating accurate recovery of operators, velocity fields, extrinsic curvature, and spatially dependent drift and diffusion coefficients.

math.NA↗

arXiv2024

Potential of quantum scientific machine learning applied to weather modelling

In this work we explore how quantum scientific machine learning can be used to tackle the challenge of weather modelling. Using parameterised quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of 4{\deg}. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a $3^{\text{rd}}$ order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. Whilst challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.

quant-ph↗

arXiv2022

Harmonic (Quantum) Neural Networks

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.

cs.LG↗

arXiv2021

Quantum Model-Discovery

Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime, where deep and wide quantum circuits can be used to solve large linear systems like partial differential equations (PDEs) efficiently. Recently, variational approaches to solving non-linear PDEs also with near-term quantum devices were proposed. One of the most promising general approaches is based on recent developments in the field of scientific machine learning for solving PDEs. We extend the applicability of near-term quantum computers to more general scientific machine learning tasks, including the discovery of differential equations from a dataset of measurements. We use differentiable quantum circuits (DQCs) to solve equations parameterized by a library of operators, and perform regression on a combination of data and equations. Our results show a promising path to Quantum Model Discovery (QMoD), on the interface between classical and quantum machine learning approaches. We demonstrate successful parameter inference and equation discovery using QMoD on different systems including a second-order, ordinary differential equation and a non-linear, partial differential equation.

quant-ph↗

arXiv2015

Asymmetrical inheritance of plasmids depends on dynamic cellular geometry and volume exclusion effects

The asymmetrical inheritance of plasmid DNA, as well as other cellular components, has been shown to be involved in replicative aging. In Saccharomyces cerevisiae, there is an ongoing debate regarding the mechanisms underlying this important asymmetry. Currently proposed models suggest it is established via diffusion, but differ on whether a diffusion barrier is necessary or not. However, no study so far incorporated key aspects to segregation, such as dynamic morphology changes throughout anaphase or plasmids size. Here, we determine the distinct effects and contributions of individual cellular variability, plasmid volume and moving boundaries in the asymmetric segregation of plasmids. We do this by measuring cellular nuclear geometries and plasmid diffusion rates with confocal microscopy, subsequently incorporating this data into a growing domain stochastic spatial simulator. Our modelling and simulations confirms that plasmid asymmetrical inheritance does not require an active barrier to diffusion, and provides a full analysis on plasmid size effects.

q-bio.SC↗

arXiv2014

Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries

Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and can highly bias conclusions from simulation studies. In this work, we present an intuitive algorithm for particle-based diffusion in and on moving boundaries, for both point particles and spherical particles. We first benchmark in appropriate scenarios our proposed stochastic method against solutions of partial differential equations, and further demonstrate that moving boundaries can give rise to super diffusive motion as well as time-inhomogeneous reaction rates. Finally, we conduct a numerical experiment representing photobleaching of diffusing fluorescent proteins in dividing Saccharomyces cerevisiae cells to demonstrate that moving boundaries might cause important effects neglected in previously published studies.

q-bio.QM↗