Hrishikesh Viswanath

Hrishikesh Viswanath, Yue Chang, Aleksey Panas et al.

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM) mitigates this cost by evolving low-dimensional latent representations of the underlying system. While neural ROMs enable querying solutions from latent states at arbitrary spatial points, their latent states typically represent the global domain and struggle to capture localized, highly dynamic behaviors such as fluids. We propose a sampling-based reduction framework that evolves Lagrangian systems directly in physical space over the particles themselves, reducing the number of active degrees of freedom via data-driven neural PDE operators. To enable querying at arbitrary spatial locations, we introduce a learnable kernel parameterization that uses local spatial information from time-evolved sample particles to infer the underlying solution manifold. Empirically, our approach achieves a 6.6x to 32x reduction in input dimensionality while maintaining high-fidelity evaluations across diverse Lagrangian regimes, including fluid flows, granular media, and elastoplastic dynamics. We refer to this framework as GIOROM (Geometry-Informed Reduced-Order Modeling). All code and data are available at: https://github.com/HrishikeshVish/GIOROM

Hrishikesh Viswanath, Juanwu Lu, S. Talha Bukhari et al.

Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

Md Ashiqur Rahman, Jasorsi Ghosh, Hrishikesh Viswanath et al.

We address the problem of generating 3D human motions in dyadic activities. In contrast to the concurrent works, which mainly focus on generating the motion of a single actor from the textual description, we generate the motion of one of the actors from the motion of the other participating actor in the action. This is a particularly challenging, under-explored problem, that requires learning intricate relationships between the motion of two actors participating in an action and also identifying the action from the motion of one actor. To address these, we propose partner conditioned motion operator (PaCMO), a neural operator-based generative model which learns the distribution of human motion conditioned by the partner's motion in function spaces through adversarial training. Our model can handle long unlabeled action sequences at arbitrary time resolution. We also introduce the "Functional Frechet Inception Distance" ($F^2ID$) metric for capturing similarity between real and generated data for function spaces. We test PaCMO on NTU RGB+D and DuetDance datasets and our model produces realistic results evidenced by the $F^2ID$ score and the conducted user study.

Baris Sarper Tezcan, Hrishikesh Viswanath, Rubab Saher et al.

Urban areas are increasingly vulnerable to thermal extremes driven by rapid urbanization and climate change. Traditionally, thermal extremes have been monitored using Earth-observing satellites and numerical modeling frameworks. For example, land surface temperature derived from Landsat or Sentinel imagery is commonly used to characterize surface heating patterns. These approaches operate as forward models, translating radiative observations or modeled boundary conditions into estimates of surface thermal states. While forward models can predict land surface temperature from vegetation and urban form, the inverse problem of determining spatial vegetation configurations that achieve a desired regional temperature shift remains largely unexplored. This task is inherently underdetermined, as multiple spatial vegetation patterns can yield similar aggregated temperature responses. Conventional regression and deterministic neural networks fail to capture this ambiguity and often produce averaged solutions, particularly under data-scarce conditions. We propose a conflated inverse modeling framework that combines a predictive forward model with a diffusion-based generative inverse model to produce diverse, physically plausible image-based vegetation patterns conditioned on specific temperature goals. Our framework maintains control over thermal outcomes while enabling diverse spatial vegetation configurations, even when such combinations are absent from training data. Altogether, this work introduces a controllable inverse modeling approach for urban climate adaptation that accounts for the inherent diversity of the problem. Code is available at the GitHub repository.

Hrishikesh Viswanath, Tianyi Zhang

Recent studies have demonstrated that large pretrained language models (LLMs) such as BERT and GPT-2 exhibit biases in token prediction, often inherited from the data distributions present in their training corpora. In response, a number of mathematical frameworks have been proposed to quantify, identify, and mitigate these the likelihood of biased token predictions. In this paper, we present a comprehensive survey of such techniques tailored towards widely used LLMs such as BERT, GPT-2, etc. We additionally introduce Fairpy, a modular and extensible toolkit that provides plug-and-play interfaces for integrating these mathematical tools, enabling users to evaluate both pretrained and custom language models. Fairpy supports the implementation of existing debiasing algorithms. The toolkit is open-source and publicly available at: \href{https://github.com/HrishikeshVish/Fairpy}{https://github.com/HrishikeshVish/Fairpy}

Hrishikesh Viswanath, Md Ashiqur Rahman, Abhijeet Vyas et al.

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are some limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, data driven machine learning-based methods such as neural networks provide a faster, fairly accurate alternative, and have certain advantages such as discretization invariance and resolution invariance. This article aims to provide a comprehensive insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems, while also noting some of the major pitfalls of machine learning-based approaches. Furthermore, we highlight, a novel and fast machine learning-based approach (~1000x) to learning the solution operator of a PDE operator learning. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics.

Hrishikesh Viswanath, Hong Chul Nam, Xi Deng et al.

Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due to higher-order derivatives. To tackle this issue, we propose an alternative approach using Monte Carlo approaches to estimate the solution to the PDE as a stochastic process for weak supervision during training. Leveraging the Walk-on-Spheres method, we introduce a learning scheme called \emph{Walk-on-Spheres Neural Operator (WoS-NO)} which uses weak supervision from WoS to train any given neural operator. We propose to amortize the cost of Monte Carlo walks across the distribution of PDE instances using stochastic representations from the WoS algorithm to generate cheap, noisy, estimates of the PDE solution during training. This is formulated into a data-free physics-informed objective where a neural operator is trained to regress against these weak supervisions, allowing the operator to learn a generalized solution map for an entire family of PDEs. This strategy does not require expensive pre-computed datasets, avoids computing higher-order derivatives for loss functions that are memory-intensive and unstable, and demonstrates zero-shot generalization to novel PDE parameters and domains. Experiments show that for the same number of training steps, our method exhibits up to 8.75$\times$ improvement in $L_2$-error compared to standard physics-informed training schemes, up to 6.31$\times$ improvement in training speed, and reductions of up to 2.97$\times$ in GPU memory consumption. We present the code at https://github.com/neuraloperator/WoS-NO

Hrishikesh Viswanath, Md Ashiqur Rahman, Rashmi Bhaskara et al.

We present, AdaFNIO - Adaptive Fourier Neural Interpolation Operator, a neural operator-based architecture to perform video frame interpolation. Current deep learning based methods rely on local convolutions for feature learning and suffer from not being scale-invariant, thus requiring training data to be augmented through random flipping and re-scaling. On the other hand, AdaFNIO, learns the features in the frames, independent of input resolution, through token mixing and global convolution in the Fourier space or the spectral domain by using Fast Fourier Transform (FFT). We show that AdaFNIO can produce visually smooth and accurate results. To evaluate the visual quality of our interpolated frames, we calculate the structural similarity index (SSIM) and Peak Signal to Noise Ratio (PSNR) between the generated frame and the ground truth frame. We provide the quantitative performance of our model on Vimeo-90K dataset, DAVIS, UCF101 and DISFA+ dataset.

Hrishikesh Viswanath, Aneesh Bhattacharya, Pascal Jutras-Dubé et al.

Affect is an emotional characteristic encompassing valence, arousal, and intensity, and is a crucial attribute for enabling authentic conversations. While existing text-to-speech (TTS) and speech-to-speech systems rely on strength embedding vectors and global style tokens to capture emotions, these models represent emotions as a component of style or represent them in discrete categories. We propose AffectEcho, an emotion translation model, that uses a Vector Quantized codebook to model emotions within a quantized space featuring five levels of affect intensity to capture complex nuances and subtle differences in the same emotion. The quantized emotional embeddings are implicitly derived from spoken speech samples, eliminating the need for one-hot vectors or explicit strength embeddings. Experimental results demonstrate the effectiveness of our approach in controlling the emotions of generated speech while preserving identity, style, and emotional cadence unique to each speaker. We showcase the language-independent emotion modeling capability of the quantized emotional embeddings learned from a bilingual (English and Chinese) speech corpus with an emotion transfer task from a reference speech to a target speech. We achieve state-of-art results on both qualitative and quantitative metrics.

Hrishikesh Viswanath, Andrey Shor, Yoshimasa Kitaguchi

This paper discusses a crowdsourcing based method that we designed to quantify the importance of different attributes of a dataset in determining the outcome of a classification problem. This heuristic, provided by humans acts as the initial weight seed for machine learning models and guides the model towards a better optimal during the gradient descent process. Often times when dealing with data, it is not uncommon to deal with skewed datasets, that over represent items of certain classes, while underrepresenting the rest. Skewed datasets may lead to unforeseen issues with models such as learning a biased function or overfitting. Traditional data augmentation techniques in supervised learning include oversampling and training with synthetic data. We introduce an experimental approach to dealing with such unbalanced datasets by including humans in the training process. We ask humans to rank the importance of features of the dataset, and through rank aggregation, determine the initial weight bias for the model. We show that collective human bias can allow ML models to learn insights about the true population instead of the biased sample. In this paper, we use two rank aggregator methods Kemeny Young and the Markov Chain aggregator to quantify human opinion on importance of features. This work mainly tests the effectiveness of human knowledge on binary classification (Popular vs Not-popular) problems on two ML models: Deep Neural Networks and Support Vector Machines. This approach considers humans as weak learners and relies on aggregation to offset individual biases and domain unfamiliarity.

Hrishikesh Viswanath, Md Ashiqur Rahman, Chi Lin et al.

Accurate and efficient 3D mapping of large-scale outdoor environments from LiDAR measurements is a fundamental challenge in robotics, particularly towards ensuring smooth and artifact-free surface reconstructions. Although the state-of-the-art methods focus on memory-efficient neural representations for high-fidelity surface generation, they often fail to produce artifact-free manifolds, with artifacts arising due to noisy and sparse inputs. To address this issue, we frame surface mapping as a physics-informed energy optimization problem, enforcing surface smoothness by optimizing an energy functional that penalizes sharp surface ridges. Specifically, we propose a deep learning based approach that learns the signed distance field (SDF) of the surface manifold from raw LiDAR point clouds using a physics-informed loss function that optimizes the $L_2$-Hessian energy of the surface. Our learning framework includes a hierarchical octree based input feature encoding and a multi-scale neural network to iteratively refine the signed distance field at different scales of resolution. Lastly, we introduce a test-time refinement strategy to correct topological inconsistencies and edge distortions that can arise in the generated mesh. We propose a \texttt{CUDA}-accelerated least-squares optimization that locally adjusts vertex positions to enforce feature-preserving smoothing. We evaluate our approach on large-scale outdoor datasets and demonstrate that our approach outperforms current state-of-the-art methods in terms of improved accuracy and smoothness. Our code is available at \href{https://github.com/HrishikeshVish/HessianForge/}{https://github.com/HrishikeshVish/HessianForge/}

P Preethi, Hrishikesh Viswanath

This paper is a presentation of a new method for denoising images using Haralick features and further segmenting the characters using artificial neural networks. The image is divided into kernels, each of which is converted to a GLCM (Gray Level Co-Occurrence Matrix) on which a Haralick Feature generation function is called, the result of which is an array with fourteen elements corresponding to fourteen features The Haralick values and the corresponding noise/text classification form a dictionary, which is then used to de-noise the image through kernel comparison. Segmentation is the process of extracting characters from a document and can be used when letters are separated by white space, which is an explicit boundary marker. Segmentation is the first step in many Natural Language Processing problems. This paper explores the process of segmentation using Neural Networks. While there have been numerous methods to segment characters of a document, this paper is only concerned with the accuracy of doing so using neural networks. It is imperative that the characters be segmented correctly, for failing to do so will lead to incorrect recognition by Natural language processing tools. Artificial Neural Networks was used to attain accuracy of upto 89%. This method is suitable for languages where the characters are delimited by white space. However, this method will fail to provide acceptable results when the language heavily uses connected letters. An example would be the Devanagari script, which is predominantly used in northern India.

P Preethi, Hrishikesh Viswanath

This work presents a comparison of machine learning algorithms that are implemented to segment the characters of text presented as an image. The algorithms are designed to work on degraded documents with text that is not aligned in an organized fashion. The paper investigates the use of Support Vector Machines, K-Nearest Neighbor algorithm and an Encoder Network to perform the operation of character spotting. Character Spotting involves extracting potential characters from a stream of text by selecting regions bound by white space.