Convergence of Upwind Finite Difference Schemes for a Scalar Conservation Law with Indefinite Discontinuities in the Flux Function. - Siddhartha Mishra (SIAM J. Numer. Anal., 2005)

Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function. - Adimurthi; Siddhartha Mishra; G. D. Veerappa Gowda (Math. Comput., 2007)

Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes. - Adimurthi; Siddhartha Mishra; G. D. Veerappa Gowda (Networks Heterog. Media, 2007)

On the upstream mobility scheme for two-phase flow in porous media - Siddhartha Mishra; Jérôme Jaffré (CoRR, 2009)

Shock Capturing Artificial Dissipation for High-Order Finite Difference Schemes. - Magnus Svärd; Siddhartha Mishra (J. Sci. Comput., 2009)

Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. - Kenneth H. Karlsen; Siddhartha Mishra; Nils Henrik Risebro (Math. Comput., 2009)

Convergence of finite volume schemes for triangular systems of conservation laws. - Kenneth H. Karlsen; Siddhartha Mishra; Nils Henrik Risebro (Numerische Mathematik, 2009)

Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws. - Giuseppe Maria Coclite; Siddhartha Mishra; Nils Henrik Risebro (Math. Comput., 2010)

Static Load Balancing for Multi-level Monte Carlo Finite Volume Solvers. - Jonas Sukys; Siddhartha Mishra; Christoph Schwab (PPAM (1), 2011)

Implicit-explicit schemes for flow equations with stiff source terms. - Magnus Svärd; Siddhartha Mishra (J. Comput. Appl. Math., 2011)

Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography. - Ulrik S. Fjordholm; Siddhartha Mishra; Eitan Tadmor (J. Comput. Phys., 2011)

Constraint Preserving Schemes Using Potential-Based Fluxes. II. Genuinely Multidimensional Systems of Conservation Laws. - Siddhartha Mishra; Eitan Tadmor (SIAM J. Numer. Anal., 2011)

Vorticity Preserving Finite Volume Schemes for the Shallow Water Equations. - Ulrik S. Fjordholm; Siddhartha Mishra (SIAM J. Sci. Comput., 2011)

Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions. - Siddhartha Mishra; Christoph Schwab; Jonas Sukys (J. Comput. Phys., 2012)

Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations. - Harish Kumar 001; Siddhartha Mishra (J. Sci. Comput., 2012)

Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data. - Siddhartha Mishra; Christoph Schwab (Math. Comput., 2012)

Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws. - Ulrik S. Fjordholm; Siddhartha Mishra; Eitan Tadmor (SIAM J. Numer. Anal., 2012)

Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions. - Siddhartha Mishra; Christoph Schwab; Jonas Sukys (SIAM J. Sci. Comput., 2012)

ENO Reconstruction and ENO Interpolation Are Stable. - Ulrik S. Fjordholm; Siddhartha Mishra; Eitan Tadmor (Found. Comput. Math., 2013)

Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. - Giuseppe Maria Coclite; Lorenzo di Ruvo; Jan Ernest; Siddhartha Mishra (Networks Heterog. Media, 2013)

Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems. - Manuel J. Castro; Ulrik S. Fjordholm; Siddhartha Mishra; Carlos Parés Madroñal (SIAM J. Numer. Anal., 2013)

Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws. - Siddhartha Mishra; Christoph Schwab; Jonas Sukys (Uncertainty Quantification in Computational Fluid Dynamics, 2013)

Numerical methods with controlled dissipation for small-scale dependent shocks. - Philippe G. LeFloch; Siddhartha Mishra (Acta Numer., 2014)

Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws. - Andreas Hiltebrand; Siddhartha Mishra (Numerische Mathematik, 2014)

Schemes with Well-Controlled Dissipation. - Jan Ernest; Philippe G. LeFloch; Siddhartha Mishra (SIAM J. Numer. Anal., 2015)

On the computation of measure-valued solutions. - Ulrik S. Fjordholm; Siddhartha Mishra; Eitan Tadmor (Acta Numer., 2016)

Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium. - Siddhartha Mishra; Christoph Schwab; Jonas Sukys (J. Comput. Phys., 2016)

Numerical Solution of Scalar Conservation Laws with Random Flux Functions. - Siddhartha Mishra; Nils Henrik Risebro; Christoph Schwab; Svetlana V. Tokareva (SIAM/ASA J. Uncertain. Quantification, 2016)

Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography. - Andreas Hiltebrand; Siddhartha Mishra (Networks Heterog. Media, 2016)

On a Model for the Evolution of Morphogens in a Growing Tissue. - Giuseppe Maria Coclite; M. M. Coclite; Siddhartha Mishra (SIAM J. Math. Anal., 2016)

Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws. - Ulrik S. Fjordholm; Roger Käppeli; Siddhartha Mishra; Eitan Tadmor (Found. Comput. Math., 2017)

A machine learning framework for data driven acceleration of computations of differential equations. - Siddhartha Mishra (CoRR, 2018)

Numerical Approximation of Statistical Solutions of Scalar Conservation Laws. - Ulrik S. Fjordholm; Kjetil O. Lye; Siddhartha Mishra (SIAM J. Numer. Anal., 2018)

Automatic Identification of Mixed Retinal Cells in Time-Lapse Fluorescent Microscopy Images using High-Dimensional DBSCAN. - Divya Spoorthy; Shanmukh Reddy Manne; Vaibhav Dhyani; Sarpras Swain; Shahna Shahulhameed; Siddhartha Mishra; Inderjeet Kaur; Lopamudra Giri; Soumya Jana (EMBC, 2019)

Statistical solutions of hyperbolic systems of conservation laws: numerical approximation. - Ulrik Skre Fjordholm; Kjetil O. Lye; Siddhartha Mishra; Franziska Weber (CoRR, 2019)

Statistical solutions of the incompressible Euler equations. - Samuel Lanthaler; Siddhartha Mishra; Carlos Parés-Pulido (CoRR, 2019)

A Multi-level procedure for enhancing accuracy of machine learning algorithms. - Kjetil O. Lye; Siddhartha Mishra; Roberto Molinaro (CoRR, 2019)

On the approximation of rough functions with deep neural networks. - Tim De Ryck; Siddhartha Mishra; Deep Ray (CoRR, 2019)

On the conservation of energy in two-dimensional incompressible flows. - Samuel Lanthaler; Siddhartha Mishra; Carlos Parés-Pulido (CoRR, 2020)

Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs. - Siddhartha Mishra; Roberto Molinaro (CoRR, 2020)

Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs II: A class of inverse problems. - Siddhartha Mishra; Roberto Molinaro (CoRR, 2020)

Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks. - Kjetil O. Lye; Siddhartha Mishra; Deep Ray; Praveen Chandrasekhar (CoRR, 2020)

Physics Informed Neural Networks for Simulating Radiative Transfer. - Siddhartha Mishra; Roberto Molinaro (CoRR, 2020)

On the Convergence of the Spectral Viscosity Method for the Two-Dimensional Incompressible Euler Equations with Rough Initial Data. - Samuel Lanthaler; Siddhartha Mishra (Found. Comput. Math., 2020)

Deep learning observables in computational fluid dynamics. - Kjetil O. Lye; Siddhartha Mishra; Deep Ray (J. Comput. Phys., 2020)

Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies. - T. Konstantin Rusch; Siddhartha Mishra (ICLR, 2021)

UnICORNN: A recurrent model for learning very long time dependencies. - T. Konstantin Rusch; Siddhartha Mishra (ICML, 2021)

Error estimates for DeepOnets: A deep learning framework in infinite dimensions. - Samuel Lanthaler; Siddhartha Mishra; George Em Karniadakis (CoRR, 2021)

Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs. - Genming Bai; Ujjwal Koley; Siddhartha Mishra; Roberto Molinaro (CoRR, 2021)

On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems. - Samuel Lanthaler; Siddhartha Mishra; Franziska Weber (CoRR, 2021)

Well-posedness of Bayesian inverse problems for hyperbolic conservation laws. - Siddhartha Mishra; David Ochsner; Adrian Montgomery Ruf; Franziska Weber (CoRR, 2021)

A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer. - Gioele Janett; Oskar Steiner; Ernest Alsina Ballester; Luca Belluzzi; Siddhartha Mishra (CoRR, 2021)

On Universal Approximation and Error Bounds for Fourier Neural Operators. - Nikola B. Kovachki; Samuel Lanthaler; Siddhartha Mishra (J. Mach. Learn. Res., 2021)

On the approximation of functions by tanh neural networks. - Tim De Ryck; Samuel Lanthaler; Siddhartha Mishra (Neural Networks, 2021)

Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences. - Siddhartha Mishra; T. Konstantin Rusch (SIAM J. Numer. Anal., 2021)

Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks. - Marcello Longo; Siddhartha Mishra; T. Konstantin Rusch; Christoph Schwab (SIAM J. Sci. Comput., 2021)

An Evaluative Measure of Clustering Methods Incorporating Hyperparameter Sensitivity. - Siddhartha Mishra; Nicholas Monath; Michael Boratko; Ariel Kobren; Andrew McCallum (AAAI, 2022)

Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings. - Shib Sankar Dasgupta; Michael Boratko; Siddhartha Mishra; Shriya Atmakuri; Dhruvesh Patel; Xiang Li 069; Andrew McCallum (ACL (1), 2022)

Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks. - Yizhong Wang; Swaroop Mishra; Pegah Alipoormolabashi; Yeganeh Kordi; Amirreza Mirzaei; Atharva Naik; Arjun Ashok; Arut Selvan Dhanasekaran; Anjana Arunkumar; David Stap; Eshaan Pathak; Giannis Karamanolakis; et al. (EMNLP, 2022)

Long Expressive Memory for Sequence Modeling. - T. Konstantin Rusch; Siddhartha Mishra; N. Benjamin Erichson; Michael W. Mahoney (ICLR, 2022)

Graph-Coupled Oscillator Networks. - T. Konstantin Rusch; Ben Chamberlain 001; James Rowbottom; Siddhartha Mishra; Michael M. Bronstein (ICML, 2022)

Generic bounds on the approximation error for physics-informed (and) operator learning. - Tim De Ryck; Siddhartha Mishra (NeurIPS, 2022)

Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs. - Tim De Ryck; Siddhartha Mishra (Adv. Comput. Math., 2022)

Error estimates for physics informed neural networks approximating the Navier-Stokes equations. - Tim De Ryck; Ameya D. Jagtap; Siddhartha Mishra (CoRR, 2022)

Benchmarking Generalization via In-Context Instructions on 1, 600+ Language Tasks. - Yizhong Wang; Swaroop Mishra; Pegah Alipoormolabashi; Yeganeh Kordi; Amirreza Mirzaei; Anjana Arunkumar; Arjun Ashok; Arut Selvan Dhanasekaran; Atharva Naik; David Stap; Eshaan Pathak; Giannis Karamanolakis; et al. (CoRR, 2022)

Variable-Input Deep Operator Networks. - Michael Prasthofer; Tim De Ryck; Siddhartha Mishra (CoRR, 2022)

Agnostic Physics-Driven Deep Learning. - Benjamin Scellier; Siddhartha Mishra; Yoshua Bengio; Yann Ollivier (CoRR, 2022)

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws. - Tim De Ryck; Siddhartha Mishra (CoRR, 2022)

Finite basis physics-informed neural networks as a Schwarz domain decomposition method. - Victorita Dolean; Alexander Heinlein; Siddhartha Mishra; Ben Moseley (CoRR, 2022)

Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities. - Samuel Lanthaler; Roberto Molinaro; Patrik Hadorn; Siddhartha Mishra (ICLR, 2023)

Gradient Gating for Deep Multi-Rate Learning on Graphs. - T. Konstantin Rusch; Benjamin Paul Chamberlain; Michael W. Mahoney; Michael M. Bronstein; Siddhartha Mishra (ICLR, 2023)

Neural Inverse Operators for Solving PDE Inverse Problems. - Roberto Molinaro; Yunan Yang; Björn Engquist; Siddhartha Mishra (ICML, 2023)

Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning. - Francesca Bartolucci; Emmanuel de Bézenac; Bogdan Raonic; Roberto Molinaro; Siddhartha Mishra; Rima Alaifari (NeurIPS, 2023)

Neural Oscillators are Universal. - Samuel Lanthaler; T. Konstantin Rusch; Siddhartha Mishra (NeurIPS, 2023)

Convolutional Neural Operators for robust and accurate learning of PDEs. - Bogdan Raonic; Roberto Molinaro; Tim De Ryck; Tobias Rohner; Francesca Bartolucci; Rima Alaifari; Siddhartha Mishra; Emmanuel de Bézenac (NeurIPS, 2023)

Convolutional Neural Operators. - Bogdan Raonic; Roberto Molinaro; Tobias Rohner; Siddhartha Mishra; Emmanuel de Bézenac (CoRR, 2023)

Multi-Scale Message Passing Neural PDE Solvers. - Léonard Equer; T. Konstantin Rusch; Siddhartha Mishra (CoRR, 2023)

A Survey on Oversmoothing in Graph Neural Networks. - T. Konstantin Rusch; Michael M. Bronstein; Siddhartha Mishra (CoRR, 2023)

A Monte-Carlo ab-initio algorithm for the multiscale simulation of compressible multiphase flows. - Marco Petrella; Rémi Abgrall; Siddhartha Mishra (CoRR, 2023)

Vandermonde Neural Operators. - Levi E. Lingsch; Mike Yan Michelis; Sirani M. Perera; Robert K. Katzschmann; Siddhartha Mishra (CoRR, 2023)

Are Neural Operators Really Neural Operators? Frame Theory Meets Operator Learning. - Francesca Bartolucci; Emmanuel de Bézenac; Bogdan Raonic; Roberto Molinaro; Siddhartha Mishra; Rima Alaifari (CoRR, 2023)

Multilevel domain decomposition-based architectures for physics-informed neural networks. - Victorita Dolean; Alexander Heinlein; Siddhartha Mishra; Ben Moseley (CoRR, 2023)

A universal approximation theorem for nonlinear resistive networks. - Benjamin Scellier; Siddhartha Mishra (CoRR, 2023)

On the discrete equation model for compressible multiphase fluid flows. - Marco Petrella; Rémi Abgrall; Siddhartha Mishra (J. Comput. Phys., 2023)

An operator preconditioning perspective on training in physics-informed machine learning. - Tim De Ryck; Florent Bonnet; Siddhartha Mishra; Emmanuel de Bézenac (ICLR, 2024)

Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains. - Levi E. Lingsch; Mike Yan Michelis; Emmanuel de Bézenac; Sirani M. Perera; Robert K. Katzschmann; Siddhartha Mishra (ICML, 2024)

SmallToLarge (S2L): Scalable Data Selection for Fine-tuning Large Language Models by Summarizing Training Trajectories of Small Models. - Yu Yang 007; Siddhartha Mishra; Jeffrey N. Chiang; Baharan Mirzasoleiman (NeurIPS, 2024)

Poseidon: Efficient Foundation Models for PDEs. - Maximilian Herde; Bogdan Raonic; Tobias Rohner; Roger Käppeli; Roberto Molinaro; Emmanuel de Bézenac; Siddhartha Mishra (NeurIPS, 2024)

FUSE: Fast Unified Simulation and Estimation for PDEs. - Levi E. Lingsch; Dana Grund; Siddhartha Mishra; Georgios Kissas (NeurIPS, 2024)

Efficient Computation of Large-Scale Statistical Solutions to Incompressible Fluid Flows. - Tobias Rohner; Siddhartha Mishra (PASC, 2024)

Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning. - Tim De Ryck; Siddhartha Mishra (Acta Numer., 2024)

Generative AI for fast and accurate Statistical Computation of Fluids. - Roberto Molinaro; Samuel Lanthaler; Bogdan Raonic; Tobias Rohner; Victor Armegioiu; Zhong Yi Wan; Fei Sha; Siddhartha Mishra; Leonardo Zepeda-Núñez (CoRR, 2024)

S7: Selective and Simplified State Space Layers for Sequence Modeling. - Taylan Soydan; Nikola Zubic; Nico Messikommer; Siddhartha Mishra; Davide Scaramuzza 001 (CoRR, 2024)

Overlapping Schwarz Preconditioners for Randomized Neural Networks with Domain Decomposition. - Yong Shang; Alexander Heinlein; Siddhartha Mishra; Fei Wang (CoRR, 2024)

On the Vanishing Viscosity Limit of Statistical Solutions of the Incompressible Navier-Stokes Equations. - Ulrik Skre Fjordholm; Siddhartha Mishra; Franziska Weber (SIAM J. Math. Anal., 2024)

wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws. - Tim De Ryck; Siddhartha Mishra; Roberto Molinaro (SIAM J. Numer. Anal., 2024)

How does over-squashing affect the power of GNNs? - Francesco Di Giovanni; T. Konstantin Rusch; Michael M. Bronstein; Andreea Deac; Marc Lackenby; Siddhartha Mishra; Petar Velickovic (Trans. Mach. Learn. Res., 2024)

Laplacian deep ensembles: Methodology and application in predicting dUT1 considering geophysical fluids. - Mostafa Kiani Shahvandi; Siddhartha Mishra; Benedikt Soja (Comput. Geosci., 2025)

NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery. - Sergei Garmaev; Siddhartha Mishra; Olga Fink (CoRR, 2025)

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs. - Tim De Ryck; Siddhartha Mishra; Y. Shang; F. Wang (CoRR, 2025)

RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains. - Sepehr Mousavi; Shizheng Wen; Levi E. Lingsch; Maximilian Herde; Bogdan Raonic; Siddhartha Mishra (CoRR, 2025)

Neuro-Symbolic AI for Analytical Solutions of Differential Equations. - Orestis Oikonomou; Levi E. Lingsch; Dana Grund; Siddhartha Mishra; Georgios Kissas (CoRR, 2025)

Data-Driven, ML-assisted Approaches to Problem Well-Posedness. - Tom Bertalan; George A. Kevrekidis; Eleni D. Koronaki; Siddhartha Mishra; Elizaveta Rebrova; Yannis G. Kevrekidis (CoRR, 2025)

Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains. - Shizheng Wen; Arsh Kumbhat; Levi E. Lingsch; Sepehr Mousavi; Yizhou Zhao; Praveen Chandrashekar; Siddhartha Mishra (CoRR, 2025)

Rectified Flows for Fast Multiscale Fluid Flow Modeling. - Victor Armegioiu; Yannick Ramic; Siddhartha Mishra (CoRR, 2025)

Finetuning a Weather Foundation Model with Lightweight Decoders for Unseen Physical Processes. - Fanny Lehmann; Firat Ozdemir; Benedikt Soja; Torsten Hoefler; Siddhartha Mishra; Sebastian Schemm (CoRR, 2025)

Functional Neural Wavefunction Optimization. - Victor Armegioiu; Juan Carrasquilla; Siddhartha Mishra; Johannes Müller; Jannes Nys; Marius Zeinhofer; Hang Zhang (CoRR, 2025)