Akash Anand

Akash Anand, Aditya Agarwal, Leslie Pack Kaelbling · mila, mit

Robotic manipulation tasks require 3D mesh reconstructions of varying quality: dexterous manipulation demands fine-grained surface detail, while collision-free planning tolerates coarser representations. Multiple reconstruction methods offer different cost-quality tradeoffs, from Image-to-3D models - whose output quality depends heavily on the input viewpoint - to view-invariant methods such as structured light scanning. Querying all models is computationally prohibitive, motivating per-input model selection. We propose SCOUT, a novel routing framework that decouples reconstruction scores into two components: (1) the relative performance of viewpoint-dependent models, captured by a learned probability distribution, and (2) the overall image difficulty, captured by a scalar partition function estimate. As the learned network operates only over the viewpoint-dependent models, view-invariant pipelines can be added, removed, or reconfigured without retraining. SCOUT also supports arbitrary cost constraints at inference time, accommodating the multi-dimensional cost constraints common in robotics. We evaluate on the Google Scanned Objects, BigBIRD, and YCB datasets under multiple mesh quality metrics, demonstrating consistent improvements over routing baselines adapted from the LLM literature across various cost constraints. We further validate the framework through robotic grasping and dexterous manipulation experiments. We release the code and additional results on our website.

Ambuj Pandey, Akash Anand

In recent years, several fast solvers for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by penetrable inhomogeneous obstacles, have been proposed. While many of these fast methodologies exhibit rapid convergence for smoothly varying scattering configurations, the rate for most of them reduce to either linear or quadratic when material properties are allowed to jump across the interface. A notable exception to this is a recently introduced Nyström scheme [J. Comput. Phys., 311 (2016), 258--274] that utilizes a specialized quadrature in the boundary region for a high-order treatment of the material interface. In this text, we present a solution framework that relies on the specialized boundary integrator to enhance the convergence rate of other fast, low order methodologies without adding to their computational complexity of $O(N \log N)$ for an $N$-point discretization. In particular, to demonstrate the efficacy of the proposed framework, we explain its implementation to enhance the order to convergence of two schemes, one introduced by Duan and Rokhlin [J. Comput. Phys., 228(6) (2009), 2152--2174] that is based on a pre-corrected trapezoidal rule while the other by Bruno and Hyde [J. Comput. Phys., 200(2) (2004), 670--694] which relies on a suitable decomposition of the Green's function via Addition theorem. In addition to a detailed description of these methodologies, we also present a comparative performance study of the improved versions of these two and the Nyström solver in [J. Comput. Phys., 311 (2016), 258--274] through a wide range of numerical experiments.

Akash Anand

It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the resolution of Gibbs phenomenon in recent years, a Fourier continuation (FC) based approximation scheme has been suggested by Bruno and collaborators in the context of certain PDE solvers where approximation grids used are equispaced. While the practical efficacy of FC based schemes in obtaining a high-order numerical solution of PDEs is well known, theoretical convergence analyses largely remain unavailable. The primary objective of this paper is to take a step in this direction where we analyze the convergence rates of a Fourier continuation framework for approximations based on discrete functional data coming from equispaced grids. In this context, we explore a certain two-point Hermite interpolation strategy for constructing Fourier continuations that, not only simplifies the implementation of such approximations but also makes possible a rigorous analysis of its numerical properties. In particular, we show that the approximations converge with order $r+1$ for functions coming from a subspace of $C^{r,1}([0,1])$, the space of $r$-times continuously differentiable function whose $r$th derivative is Lipschitz continuous. We also demonstrate that theoretical rates are indeed achieved in practice, through a variety of numerical experiments.

Prakash Nainwal, Akash Anand

The FC-Gram algorithm approximates non-periodic functions to high order by constructing a periodic extension with controlled boundary behavior and applying trigonometric interpolation. In this paper we introduce a generalized FC-Gram framework (GenFC), which provides greater flexibility in the construction of the blending continuation of Gram polynomials. This flexibility gives better control over the shape of the periodic extension and leads to improved approximation accuracy. We establish a convergence theorem showing that the trigonometric interpolant converges at the rate $\mathcal{O}(n^{-\min(r+β,\,d)})$ in the supremum norm on the original interval, where $r$ is the smoothness of the target function, $d$ the number of Gram polynomials, and $β\in [0,1]$ a Fourier-decay parameter. The framework and its analysis are developed so that the modified FC-Gram method of [J. Sci. Comput., 105(1):8, 2025] is recovered as a particular case. Numerical experiments confirm the predicted convergence rates and show that the added flexibility of the GenFC framework leads to improved approximation accuracy, with the gains carrying over to a Fourier continuation solver for two-point boundary value problems.

AJ Venkatakrishnan, Arjun Puranik, Akash Anand et al.

The COVID-19 pandemic demands assimilation of all available biomedical knowledge to decode its mechanisms of pathogenicity and transmission. Despite the recent renaissance in unsupervised neural networks for decoding unstructured natural languages, a platform for the real-time synthesis of the exponentially growing biomedical literature and its comprehensive triangulation with deep omic insights is not available. Here, we present the nferX platform for dynamic inference from over 45 quadrillion possible conceptual associations extracted from unstructured biomedical text, and their triangulation with Single Cell RNA-sequencing based insights from over 25 tissues. Using this platform, we identify intersections between the pathologic manifestations of COVID-19 and the comprehensive expression profile of the SARS-CoV-2 receptor ACE2. We find that tongue keratinocytes and olfactory epithelial cells are likely under-appreciated targets of SARS-CoV-2 infection, correlating with reported loss of sense of taste and smell as early indicators of COVID-19 infection, including in otherwise asymptomatic patients. Airway club cells, ciliated cells and type II pneumocytes in the lung, and enterocytes of the gut also express ACE2. This study demonstrates how a holistic data science platform can leverage unprecedented quantities of structured and unstructured publicly available data to accelerate the generation of impactful biological insights and hypotheses.

Akash Anand, Awanish Kumar Tiwari

Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for numerical solution of integral equations. Most fast techniques in this direction utilize uniform grid discretizations of the integral that facilitate the use of FFT for $O(n\log n)$ computations on a grid of size $n$. In general, however, the resulting error converges slowly with increasing $n$ when the integrand does not have a smooth periodic extension. Such extensions, in fact, are often discontinuous and, therefore, their approximations by truncated Fourier series suffer from Gibb's oscillations. In this paper, we present and analyze an $O(n\log n)$ scheme, based on a Fourier extension approach for removing such unwanted oscillations, that not only converges with high-order but is also relatively simple to implement. We include a theoretical error analysis as well as a wide variety of numerical experiments to demonstrate its efficacy.

Manish Sharma, Akash Anand, Rupika Srivastava et al.

Wearables like smartwatches which are embedded with sensors and powerful processors, provide a strong platform for development of analytics solutions in sports domain. To analyze players' games, while motion sensor based shot detection has been extensively studied in sports like Tennis, Golf, Baseball; Table Tennis and Badminton are relatively less explored due to possible less intense hand motion during shots. In our paper, we propose a novel, computationally inexpensive and real-time system for shot detection in table tennis, based on fusion of Inertial Measurement Unit (IMU) and audio sensor data embedded in a wrist-worn wearable. The system builds upon our presented methodology for synchronizing IMU and audio sensor input in time using detected shots and achieves 95.6% accuracy. To our knowledge, it is the first fusion-based solution for sports analysis in wearables. Shot detectors for other racquet sports as well as further analytics to provide features like shot classification, rally analysis and recommendations, can easily be built over our proposed solution.

Akash Anand, Jeffrey S. Ovall, Steffen Weisser

We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via Nyström discretizations of associated integral equations, allowing for curvilinear polygons and non-polynomial boundary data. Several experiments demonstrate the approximation quality of interpolated functions in these spaces.

Akash Anand, Ambuj Pandey, B. V. Rathish Kumar et al.

This text proposes a fast, rapidly convergent Nyström method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of $O(N \log N)$ for an $N$-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance in terms of both speed and accuracy are presented in this paper.