Projects | Nithin Chalapathi

2024

Scaling physics-informed hard constraints with mixture-of-experts

Nithin Chalapathi, Yiheng Du, and Aditi S. Krishnapriyan

In The Twelfth International Conference on Learning Representations, 2024

Abstract PDF Code

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve accuracy by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints, and provides greater control to scale between soft and hard constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE). Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.
Neural Spectral Methods: Self-supervised learning in the spectral domain

Yiheng Du, Nithin Chalapathi, and Aditi S. Krishnapriyan

In The Twelfth International Conference on Learning Representations, 2024

Abstract PDF Code

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval’s identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10x increase in performance speed.
Inferring Visualization Intent from Conversation

Haotian Li^*, Nithin Chalapathi^*, Huamin Qu, and 2 more authors

In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, Boise, ID, USA, 2024

Abstract PDF

During visual data analysis, users often explore visualizations one at a time, with each visualization leading to new directions of exploration. We consider a conversational approach to visualization, where users specify their needs at each step in natural language, with a visualization being returned in turn. Prior work has shown that visualization generation can be boiled down to the identification of visualization intent and visual encodings. Recognizing that the latter is a well-studied problem with standard solutions, we focus on the former, i.e., identifying visualization intent during conversation. We develop Luna, a framework that comprises a novel combination of language models adapted from BERT and rule-based inference, that together predict various aspects of visualization intent. We compare Luna with other conversational NL-to-visualization and NL-to-SQL approaches (adapted to visualization intent), including GPT-3.5 and GPT-4, and demonstrate that Luna has 14.3% higher accuracy than the state-of-the-art. We also apply Luna to a usage scenario on a dataset of police misconduct, showcasing its benefits relative to other approaches.

2021

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

Archit Rathore^*, Nithin Chalapathi^*, Sourabh Palande, and 1 more author

Computer Graphics Forum, 2021

Abstract PDF Website

Abstract Deep neural networks such as GoogLeNet, ResNet, and BERT have achieved impressive performance in tasks such as image and text classification. To understand how such performance is achieved, we probe a trained deep neural network by studying neuron activations, i.e.combinations of neuron firings, at various layers of the network in response to a particular input. With a large number of inputs, we aim to obtain a global view of what neurons detect by studying their activations. In particular, we develop visualizations that show the shape of the activation space, the organizational principle behind neuron activations, and the relationships of these activations within a layer. Applying tools from topological data analysis, we present TopoAct, a visual exploration system to study topological summaries of activation vectors. We present exploration scenarios using TopoAct that provide valuable insights into learned representations of neural networks. We expect TopoAct to give a topological perspective that enriches the current toolbox of neural network analysis, and to provide a basis for network architecture diagnosis and data anomaly detection.
Mapper Interactive: A Scalable, Extendable, and Interactive Toolbox for the Visual Exploration of High-Dimensional Data

Youjia Zhou, Nithin Chalapathi, Archit Rathore, and 2 more authors

In 2021 IEEE 14th Pacific Visualization Symposium (PacificVis), 2021

Abstract PDF Code Website

The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and visualization of high-dimensional point cloud data. It implements the mapper algorithm in an interactive, scalable, and easily extendable way, thus supporting practical data analysis. In particular, its command-line API can compute mapper graphs for 1 million points of 256 dimensions in about 3 minutes (4 times faster than the vanilla implementation). Its visual interface allows on-the-fly computation and manipulation of the mapper graph based on user-specified parameters and supports the addition of new analysis modules with a few lines of code. Mapper Interactive makes the mapper algorithm accessible to nonspecialists and accelerates topological analytics workflows.
Adaptive Covers for Mapper Graphs Using Information Criteria

Nithin Chalapathi, Youjia Zhou, and Bei Wang

In 2021 IEEE International Conference on Big Data (Big Data), 2021

Abstract PDF

The mapper construction is a widely used tool from topological data analysis in obtaining topological summaries of large, high-dimensional point cloud data. It has enjoyed great success in data science, including cancer research, sports analytics, and visualization. However, developing practical and automatic parameter selection for the mapper construction remains a challenging open problem for both the topological analysis and visualization communities. In this paper, we focus on parameter selection for the 1-dimensional skeleton of the mapper construction, called the mapper graph. Specifically, we explore how information criteria used in the X-means clustering algorithm can inform and generate adaptive covers for mapper graphs. Our approach thus makes novel progress towards automatic parameter selection for the mapper construction using information theory.

2020

Correctness-preserving Compression of Datasets and Neural Network Models

Vinu Joseph, Nithin Chalapathi, Aditya Bhaskara, and 3 more authors

In 2020 IEEE/ACM 4th International Workshop on Software Correctness for HPC Applications (Correctness), 2020

Abstract PDF

Neural networks deployed on edge devices must be efficient both in terms of their model size and the amount of data movement they cause when classifying inputs. These efficiencies are typically achieved through model compression: pruning a fully trained network model by zeroing out the weights. Given the overall challenge of neural network correctness, we argue that focusing on correctness preservation may allow the community to make measurable progress. We present a state-of-the-art model compression framework called Condensa around which we have launched correctness preservation studies. After presenting Condensa, we describe our initial efforts at understanding the effect of model compression in semantic terms, going beyond the top n% accuracy that Condensa is currently based on. We also take up the relatively unexplored direction of data compression that may help reduce data movement. We report preliminary results of learning from decompressed data to understand the effects of compression artifacts. Learning without decompressing input data also holds promise in terms of boosting efficiency, and we also report preliminary results in this regard. Our experiments centered around a state-of-the-art model compression framework called Condensa and two data compression algorithms, namely JPEG and ZFP, demonstrate the potential for employing model-and dataset compression without adversely affecting correctness.
Interactive Visualization of Interdependent Power and Water Infrastructure Operation

Han Han, Konstantinos Oikonomou, Nithin Chalapathi, and 2 more authors

In 2020 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), 2020

Abstract PDF

With increasing levels of drought across the world together with the rising demand of freshwater and energy consumption, the interdependence between power and water sectors is becoming increasingly important. However, as power and water system operators have traditionally operated their systems in isolation, there is a lack of understanding of the interdependence and interactions between these systems. This paper bridges this information gap by developing 2D and 3D visualization prototypes for interdependent power and water distribution systems. These prototypes aim to display and monitor a variety of water and energy variables, and to increase the observability and controllability for power and water distribution system operations. Visualization results show that the proposed prototypes successfully monitor the energy requirements for meeting the energy and water demands and capture operational decisions that can improve energy efficiency and reduce operating costs of interdependent systems.