arXiv subjects

Sahana Rayan

Publications and source records attributed to Sahana Rayan.

4 recordsLinked to original sources

arXiv2025

A Greedy PDE Router for Blending Neural Operators and Classical Methods

When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative solver--where, at each iteration, a solver is selected from an ensemble of solvers to leverage their complementary strengths--poses a challenging combinatorial problem. While greedy selection is desirable for its constant-factor approximation guarantee to the optimal solution under Lipschitz assumptions, it requires knowledge of the true error at each step, which is unavailable in practice. We address this by proposing an approximate greedy router that efficiently mimics a greedy approach to solver selection. Empirical results on the Poisson and convection-diffusion equations show that our method consistently reduces final error and area-under-the-curve (AUC) of the error trajectory relative to single-solver baselines and existing hybrid approaches such as HINTS. In particular, our method reaches comparable error levels in substantially fewer iterations while exhibiting more stable error decay.

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arXiv2025

Learning to Partially Defer for Sequences

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the {\em entire prediction}, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer \textit{specific outputs} of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers, News summarization, and Weather prediction.

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arXiv2024

Conformal Robust Control of Linear Systems

End-to-end engineering design pipelines, in which designs are evaluated using concurrently defined optimal controllers, are becoming increasingly common in practice. To discover designs that perform well even under the misspecification of system dynamics, such end-to-end pipelines have now begun evaluating designs with a robust control objective in place of the nominal optimal control setup. Current approaches of specifying such robust control subproblems, however, rely on hand specification of perturbations anticipated to be present upon deployment or margin methods that ignore problem structure, resulting in a lack of theoretical guarantees and overly conservative empirical performance. We, instead, propose a novel methodology for LQR systems that leverages conformal prediction to specify such uncertainty regions in a data-driven fashion. Such regions have distribution-free coverage guarantees on the true system dynamics, in turn allowing for a probabilistic characterization of the regret of the resulting robust controller. We then demonstrate that such a controller can be efficiently produced via a novel policy gradient method that has convergence guarantees. We finally demonstrate the superior empirical performance of our method over alternate robust control specifications, such as $H_{\infty}$ and LQR with multiplicative noise, across a collection of engineering control systems.

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arXiv2023

Conformal Contextual Robust Optimization

Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative uncertainty regions, often resulting in suboptimal decisionmaking. To this end, we propose Conformal-Predict-Then-Optimize (CPO), a framework for leveraging highly informative, nonconvex conformal prediction regions over high-dimensional spaces based on conditional generative models, which have the desired distribution-free coverage guarantees. Despite guaranteeing robustness, such black-box optimization procedures alone inspire little confidence owing to the lack of explanation of why a particular decision was found to be optimal. We, therefore, augment CPO to additionally provide semantically meaningful visual summaries of the uncertainty regions to give qualitative intuition for the optimal decision. We highlight the CPO framework by demonstrating results on a suite of simulation-based inference benchmark tasks and a vehicle routing task based on probabilistic weather prediction.

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