arXiv subjects

Harsh Choudhary

Publications and source records attributed to Harsh Choudhary.

7 recordsLinked to original sources

arXiv2026

Symplectic Neural Networks for Learning Non-Separable Hamiltonians

Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency. Identifying the system Hamiltonian from noisy observations of state variables is a challenging task. For simulations to faithfully reflect the long-term behavior of Hamiltonian systems, especially energy conservation, it is essential to use symplectic integrators, which preserve the system's geometric structure. This fidelity comes at a cost: implicit symplectic integrators are more computationally intensive and make backpropagation through the ODE solver non-trivial. However, by leveraging the fact that symplectic discretizations of the adjoint system yield the same sensitivities associated by backpropagation, we obtain an efficient method of training the Neural Network parameters. In our work, we explore this alternate method of HNN training under noisy observation of trajectories with our HNN model based on an implicit symplectic integrator. Computationally, a predictor-corrector based ODE solver and fixed point iteration help to mitigate the computational cost of the implicit timestepping, resulting in more efficient generation of gradient updates. We showcase the numerical advantage, in experiments, in system identification and energy preservation on a range of non-separable, chaotic systems and the efficient computation and memory complexity of our method. We also observe that the post-processing of the learned Hamiltonian using backward error analysis yields a modified Hamiltonian that is a more accurate approximation of the true Hamiltonian without the need to use more accurate discretizations of the flow map.

cs.LG↗

arXiv2025

An Alternating Direction Method of Multipliers for Topology Optimization

We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design variables, nonsmooth regularization, and non-convex objective renders the problem computationally challenging. To address this, we adopt the alternating direction method of multipliers (ADMM) framework, which enables a decomposition of the original problem into simpler subproblems that can be solved efficiently. The augmented Lagrangian formulation ensures consistency across variable updates while facilitating convergence under appropriate conditions.

math.OC↗

arXiv2025

Inexact and Stochastic Gradient Optimization Algorithms with Inertia and Hessian Driven Damping

In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can be subject to deterministic and stochastic perturbations. In the deterministic case, we show that under appropriate summability assumptions on the perturbation, our algorithm enjoys fast convergence of the objective values, of the gradients and weak convergence of the iterates toward a minimizer of the objective. In the stochastic case, assuming the perturbation is zero-mean, we can weaken our summability assumptions on the error variance and provide fast convergence of the values both in expectation and almost surely. We also improve the convergence rates from $\mathcal{O}(\cdot)$ to $o(\cdot)$ in almost sure sense. We also prove almost sure summability property of the gradients, which implies the almost sure fast convergence of the gradients towards zero. We will highlight the trade-off between fast convergence and the applicable regime on the sequence of errors in the gradient computations. We finally report some numerical results to support our findings.

math.OC↗

arXiv2025

Efficacy of Galaxy Catalogues for following up gravitational wave events

The detection of gravitational waves (GW) by the LIGO-Virgo-KAGRA (LVK) network has opened up a new era in astrophysics. The identification of the electromagnetic counterparts of GW sources is crucial for multi-messenger astronomy, one way of which is to use galaxy catalogues to guide optical follow-up observations. In this paper, we test the utility of galaxy-targeted approach with mass prioritised galaxy ranking for the ongoing LIGO O4 run. We have used the simulated results for the expected LIGO O4 events and the NED-LVS galaxy catalogue and based our study for small field of view telescopes, specifically the GROWTH-India Telescope (GIT). With the increase in sensitivity of LIGO/Virgo in the ongoing observing run O4, the expected number of total detections have gone up but most of these are also now poorly localised. We show that a larger volume covered in the same field-of-view (FoV) on the sky results in a large increase in the total number of galaxies in each FoV. A significant top-heaviness is observed in the mass-ranked list of galaxies, which still number to a few thousand in most cases. At larger distances, such high numbers of deep follow-up observations are infeasible in most cases rendering galaxy catalogues useful in limited cases, but these are still useful at lower distances where LVK detectors are currently sensitive and where galaxy completeness is higher. We also explore the effect of mass-filling to account for galaxy catalogue incompleteness at large distances. If mass-filled probabilities are considered as the metric for ranking and coverage, we find that the conventional 2D probability search performs better than a 3D galaxy catalogue (without mass-filling) based search at distances larger than 300 Mpc (upto which NED-LVS is ~70% complete), and using 3D mass times probability in each tile performs better for nearby events.

astro-ph.HE↗

arXiv2025

Low-Resource Video Super-Resolution using Memory, Wavelets, and Deformable Convolutions

The tradeoff between reconstruction quality and compute required for video super-resolution (VSR) remains a formidable challenge in its adoption for deployment on resource-constrained edge devices. While transformer-based VSR models have set new benchmarks for reconstruction quality in recent years, these require substantial computational resources. On the other hand, lightweight models that have been introduced even recently struggle to deliver state-of-the-art reconstruction. We propose a novel lightweight and parameter-efficient neural architecture for VSR that achieves state-of-the-art reconstruction accuracy with just 2.3 million parameters. Our model enhances information utilization based on several architectural attributes. Firstly, it uses 2D wavelet decompositions strategically interlayered with learnable convolutional layers to utilize the inductive prior of spatial sparsity of edges in visual data. Secondly, it uses a single memory tensor to capture inter-frame temporal information while avoiding the computational cost of previous memory-based schemes. Thirdly, it uses residual deformable convolutions for implicit inter-frame object alignment that improve upon deformable convolutions by enhancing spatial information in inter-frame feature differences. Architectural insights from our model can pave the way for real-time VSR on the edge, such as display devices for streaming data.

cs.CV↗

arXiv2024

Learning Generalized Hamiltonians using fully Symplectic Mappings

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and in particular Hamiltonian Neural Networks have emerged as a mechanism to incorporate structural inductive bias into the NN model. By ensuring physical invariances are conserved, the models exhibit significantly better sample complexity and out-of-distribution accuracy than standard NNs. Learning the Hamiltonian as a function of its canonical variables, typically position and velocity, from sample observations of the system thus becomes a critical task in system identification and long-term prediction of system behavior. However, to truly preserve the long-run physical conservation properties of Hamiltonian systems, one must use symplectic integrators for a forward pass of the system's simulation. While symplectic schemes have been used in the literature, they are thus far limited to situations when they reduce to explicit algorithms, which include the case of separable Hamiltonians or augmented non-separable Hamiltonians. We extend it to generalized non-separable Hamiltonians, and noting the self-adjoint property of symplectic integrators, we bypass computationally intensive backpropagation through an ODE solver. We show that the method is robust to noise and provides a good approximation of the system Hamiltonian when the state variables are sampled from a noisy observation. In the numerical results, we show the performance of the method concerning Hamiltonian reconstruction and conservation, indicating its particular advantage for non-separable systems.

cs.LG↗

arXiv2023

Astreaks: Astrometry of NEOs with trailed background stars

The detection and accurate astrometry of fast-moving near-Earth objects (NEOs) has been a challenge for the follow-up community. Their fast apparent motion results in streaks in sidereal images, thus affecting the telescope's limiting magnitude and astrometric accuracy. A widely adopted technique to mitigate trailing losses is non-sidereal tracking, which transfers the streaking to background reference stars. However, no existing publicly available astrometry software is configured to detect such elongated stars. We present Astreaks, a streaking source detection algorithm, to obtain accurate astrometry of NEOs in non-sidereal data. We validate the astrometric accuracy of Astreaks on 371 non-sidereally tracked images for 115 NEOs with two instrument set-ups of the GROWTH-India Telescope. The observed NEOs had V-band magnitude in the range [15, 22] with proper motion up to 140$^{\prime\prime}$/min, thus resulting in stellar streaks as high as 6.5$^\prime$ (582 pixels) in our data. Our method obtained astrometric solutions for all images with 100% success rate. The standard deviation in Observed-minus-Computed (O-C) residuals is 0.52$^{\prime\prime}$, with O-C residuals <2$^{\prime\prime}$(<1$^{\prime\prime}$) for 98.4% (84.4%) of our measurements. These are appreciable, given the pixel scale of $\sim$0.3$^{\prime\prime}$ and $\sim$0.7$^{\prime\prime}$ of our two instrument set-ups. This demonstrates that our modular and fully-automated algorithm helps improve the telescope system's limiting magnitude without compromising astrometric accuracy by enabling non-sidereal tracking on the target. This will help the NEO follow-up community cope with the accelerated discovery rates and improved sensitivity of the next-generation NEO surveys. Astreaks has been made available to the community under an open-source license.

astro-ph.IM↗