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Shirish Karande

Publications and source records attributed to Shirish Karande.

31 records · Page 2Linked to original sources
arXiv2023

HyperLoRA for PDEs

Physics-informed neural networks (PINNs) have been widely used to develop neural surrogates for solutions of Partial Differential Equations. A drawback of PINNs is that they have to be retrained with every change in initial-boundary conditions and PDE coefficients. The Hypernetwork, a model-based meta learning technique, takes in a parameterized task embedding as input and predicts the weights of PINN as output. Predicting weights of a neural network however, is a high-dimensional regression problem, and hypernetworks perform sub-optimally while predicting parameters for large base networks. To circumvent this issue, we use a low ranked adaptation (LoRA) formulation to decompose every layer of the base network into low-ranked tensors and use hypernetworks to predict the low-ranked tensors. Despite the reduced dimensionality of the resulting weight-regression problem, LoRA-based Hypernetworks violate the underlying physics of the given task. We demonstrate that the generalization capabilities of LoRA-based hypernetworks drastically improve when trained with an additional physics-informed loss component (HyperPINN) to satisfy the governing differential equations. We observe that LoRA-based HyperPINN training allows us to learn fast solutions for parameterized PDEs like Burger's equation and Navier Stokes: Kovasznay flow, while having an 8x reduction in prediction parameters on average without compromising on accuracy when compared to all other baselines.

cs.LG↗
arXiv2023

How important are specialized transforms in Neural Operators?

Simulating physical systems using Partial Differential Equations (PDEs) has become an indispensible part of modern industrial process optimization. Traditionally, numerical solvers have been used to solve the associated PDEs, however recently Transform-based Neural Operators such as the Fourier Neural Operator and Wavelet Neural Operator have received a lot of attention for their potential to provide fast solutions for systems of PDEs. In this work, we investigate the importance of the transform layers to the reported success of transform based neural operators. In particular, we record the cost in terms of performance, if all the transform layers are replaced by learnable linear layers. Surprisingly, we observe that linear layers suffice to provide performance comparable to the best-known transform-based layers and seem to do so with a compute time advantage as well. We believe that this observation can have significant implications for future work on Neural Operators, and might point to other sources of efficiencies for these architectures.

cs.LG↗
arXiv2023

Synthesis of Mathematical programs from Natural Language Specifications

Several decision problems that are encountered in various business domains can be modeled as mathematical programs, i.e. optimization problems. The process of conducting such modeling often requires the involvement of experts trained in operations research and advanced algorithms. Surprisingly, despite the significant advances in the methods for program and code synthesis, AutoML, learning to optimize etc., there has been little or no attention paid to automating the task of synthesizing mathematical programs. We imagine a scenario where the specifications for modeling, i.e. the objective and constraints are expressed in an unstructured form in natural language (NL) and the mathematical program has to be synthesized from such an NL specification. In this work we evaluate the efficacy of employing CodeT5 with data augmentation and post-processing of beams. We utilize GPT-3 with back translation for generation of synthetic examples. Further we apply rules of linear programming to score beams and correct beams based on common error patterns. We observe that with these enhancements CodeT5 base gives an execution accuracy of 0.73 which is significantly better than zero-shot execution accuracy of 0.41 by ChatGPT and 0.36 by Codex.

cs.AI↗
arXiv2023

DeepEpiSolver: Unravelling Inverse problems in Covid, HIV, Ebola and Disease Transmission

The spread of many infectious diseases is modeled using variants of the SIR compartmental model, which is a coupled differential equation. The coefficients of the SIR model determine the spread trajectories of disease, on whose basis proactive measures can be taken. Hence, the coefficient estimates must be both fast and accurate. Shaier et al. in the paper "Disease Informed Neural Networks" used Physics Informed Neural Networks (PINNs) to estimate the parameters of the SIR model. There are two drawbacks to this approach. First, the training time for PINNs is high, with certain diseases taking close to 90 hrs to train. Second, PINNs don't generalize for a new SIDR trajectory, and learning its corresponding SIR parameters requires retraining the PINN from scratch. In this work, we aim to eliminate both of these drawbacks. We generate a dataset between the parameters of ODE and the spread trajectories by solving the forward problem for a large distribution of parameters using the LSODA algorithm. We then use a neural network to learn the mapping between spread trajectories and coefficients of SIDR in an offline manner. This allows us to learn the parameters of a new spread trajectory without having to retrain, enabling generalization at test time. We observe a speed-up of 3-4 orders of magnitude with accuracy comparable to that of PINNs for 11 highly infectious diseases. Further finetuning of neural network inferred ODE coefficients using PINN further leads to 2-3 orders improvement of estimated coefficients.

cs.LG↗
arXiv2023

Symbolic Regression for PDEs using Pruned Differentiable Programs

Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to interpret, and are often treated as black-box solvers. While Symbolic Regression (SR) has been studied extensively, very few works exist which generate analytical expressions to directly perform SR for a system of PDEs. In this work, we introduce an end-to-end framework for obtaining mathematical expressions for solutions of PDEs. We use a trained PINN to generate a dataset, upon which we perform SR. We use a Differentiable Program Architecture (DPA) defined using context-free grammar to describe the space of symbolic expressions. We improve the interpretability by pruning the DPA in a depth-first manner using the magnitude of weights as our heuristic. On average, we observe a 95.3% reduction in parameters of DPA while maintaining accuracy at par with PINNs. Furthermore, on an average, pruning improves the accuracy of DPA by 7.81% . We demonstrate our framework outperforms the existing state-of-the-art SR solvers on systems of complex PDEs like Navier-Stokes: Kovasznay flow and Taylor-Green Vortex flow. Furthermore, we produce analytical expressions for a complex industrial use-case of an Air-Preheater, without suffering from performance loss viz-a-viz PINNs.

cs.LG↗
arXiv2022

Physics Informed Symbolic Networks

We introduce Physics Informed Symbolic Networks (PISN) which utilize physics-informed loss to obtain a symbolic solution for a system of Partial Differential Equations (PDE). Given a context-free grammar to describe the language of symbolic expressions, we propose to use weighted sum as continuous approximation for selection of a production rule. We use this approximation to define multilayer symbolic networks. We consider Kovasznay flow (Navier-Stokes) and two-dimensional viscous Burger's equations to illustrate that PISN are able to provide a performance comparable to PINNs across various start-of-the-art advances: multiple outputs and governing equations, domain-decomposition, hypernetworks. Furthermore, we propose Physics-informed Neurosymbolic Networks (PINSN) which employ a multilayer perceptron (MLP) operator to model the residue of symbolic networks. PINSNs are observed to give 2-3 orders of performance gain over standard PINN.

cs.LG↗
arXiv2022

Real-time Health Monitoring of Heat Exchangers using Hypernetworks and PINNs

We demonstrate a Physics-informed Neural Network (PINN) based model for real-time health monitoring of a heat exchanger, that plays a critical role in improving energy efficiency of thermal power plants. A hypernetwork based approach is used to enable the domain-decomposed PINN learn the thermal behavior of the heat exchanger in response to dynamic boundary conditions, eliminating the need to re-train. As a result, we achieve orders of magnitude reduction in inference time in comparison to existing PINNs, while maintaining the accuracy on par with the physics-based simulations. This makes the approach very attractive for predictive maintenance of the heat exchanger in digital twin environments.

cs.LG↗
arXiv2017

Layer-wise training of deep networks using kernel similarity

Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks demonstrated that with deeper layers, more simple and more accurate data representations are obtained. In this paper, we propose an approach for layer-wise training of a deep network for the supervised classification task. A transformation matrix of each layer is obtained by solving an optimization aimed at a better representation where a subsequent layer builds its representation on the top of the features produced by a previous layer. We compared the performance of our approach with a DNN trained using back-propagation which has same architecture as ours. Experimental results on the real image datasets demonstrate efficacy of our approach. We also performed kernel analysis of layer representations to validate the claim of better feature encoding.

cs.LG↗
arXiv2017

Knowledge distillation using unlabeled mismatched images

Current approaches for Knowledge Distillation (KD) either directly use training data or sample from the training data distribution. In this paper, we demonstrate effectiveness of 'mismatched' unlabeled stimulus to perform KD for image classification networks. For illustration, we consider scenarios where this is a complete absence of training data, or mismatched stimulus has to be used for augmenting a small amount of training data. We demonstrate that stimulus complexity is a key factor for distillation's good performance. Our examples include use of various datasets for stimulating MNIST and CIFAR teachers.

cs.CV↗
arXiv2016

Stamp processing with examplar features

Document digitization is becoming increasingly crucial. In this work, we propose a shape based approach for automatic stamp verification/detection in document images using an unsupervised feature learning. Given a small set of training images, our algorithm learns an appropriate shape representation using an unsupervised clustering. Experimental results demonstrate the effectiveness of our framework in challenging scenarios.

cs.CV↗
arXiv2016

Feasibility of Post-Editing Speech Transcriptions with a Mismatched Crowd

Manual correction of speech transcription can involve a selection from plausible transcriptions. Recent work has shown the feasibility of employing a mismatched crowd for speech transcription. However, it is yet to be established whether a mismatched worker has sufficiently fine-granular speech perception to choose among the phonetically proximate options that are likely to be generated from the trellis of an ASRU. Hence, we consider five languages, Arabic, German, Hindi, Russian and Spanish. For each we generate synthetic, phonetically proximate, options which emulate post-editing scenarios of varying difficulty. We consistently observe non-trivial crowd ability to choose among fine-granular options.

cs.AI↗
arXiv2008

On the Capacity Improvement of Multicast Traffic with Network Coding

In this paper, we study the contribution of network coding (NC) in improving the multicast capacity of random wireless ad hoc networks when nodes are endowed with multi-packet transmission (MPT) and multi-packet reception (MPR) capabilities. We show that a per session throughput capacity of $Θ(nT^{3}(n))$, where $n$ is the total number of nodes and T(n) is the communication range, can be achieved as a tight bound when each session contains a constant number of sinks. Surprisingly, an identical order capacity can be achieved when nodes have only MPR and MPT capabilities. This result proves that NC does not contribute to the order capacity of multicast traffic in wireless ad hoc networks when MPR and MPT are used in the network. The result is in sharp contrast to the general belief (conjecture) that NC improves the order capacity of multicast. Furthermore, if the communication range is selected to guarantee the connectivity in the network, i.e., $T(n)\ge Θ(\sqrt{\log n/n})$, then the combination of MPR and MPT achieves a throughput capacity of $Θ(\frac{\log^{3/2} n}{\sqrt{n}})$ which provides an order capacity gain of $Θ(\log^2 n)$ compared to the point-to-point multicast capacity with the same number of destinations.

cs.IT↗