13 citations · 27 across the 25 of their papers we have counts for
27 papers
Dynamic Quadtree Tokenization and Transformer for Adaptive Mesh PDE Forecasting
Yilin Zhuang, Noah Zambrano, Karthik Duraisamy
The quadratic attention cost of Vision Transformers (ViTs) forces a trade-off between spatial resolution and rollout horizon, particularly for fine-scale PDEs where shocks, reactio…
In-context learning from self-generated trajectories for adaptive model reduction
Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy
High-fidelity simulations of complex physical systems are often too expensive for repeated prediction, design, and control. Reduced-order models address this computational cost by…
Evolutionary Feature Engineering for Structured Data
Ege Onur Taga, Yilin Zhuang, M. Emrullah Ildiz +4
Large language models are increasingly used as open-ended search operators in evolutionary optimization. We introduce Evolutionary Feature Engineering (EFE), a framework for using…
History-aware adaptive reduced-order models via incremental singular value decomposition
Amirpasha Hedayat, Ali Mohaghegh, Laura Balzano +2
Reduced-order models (ROMs) can accelerate high-dimensional dynamical simulations, but their accuracy often deteriorates when online dynamics leave the regime represented by offlin…
Fully Discrete Active Flux Method based on Transported Acoustic Increments for the Compressible Euler Equations
Karthik Duraisamy
A fully discrete Active Flux method is proposed for the two-dimensional compressible Euler equations. The method builds on the evolution-operator formulation of multidimensional Ac…
Predictivity and Utility of Neural Surrogates of Multiscale PDEs
Karthik Duraisamy
Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent…
Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges
Amirpasha Hedayat, Alberto Padovan, Karthik Duraisamy
Projection-based Reduced Order Models (ROMs) are often deployed as static surrogates, which limits their practical utility once a system leaves the training manifold. We formalize…
Residual-augmented flow matching operators for probabilistic partial differential equations
Sahil Bhola, Karthik Duraisamy
Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural operators fail to characterize uncertainty,…
Attention-Enhanced Convolutional Autoencoder and Structured Delay Embeddings for Weather Prediction
Amirpasha Hedayat, Karthik Duraisamy
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient r…
Asymptotic-preserving semi-implicit finite volume scheme for Extended Magnetohydrodynamics
Yi Han Toh, Joshua Dolence, Karthik Duraisamy
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This…
Two-point Turbulence Closures in Physical Space
Noah Zambrano, Karthik Duraisamy
This work presents a predictive two-point statistical closure framework for turbulence formulated in physical space. A closure model for ensemble-averaged, incompressible homogeneo…
Foundation Models for Discovery and Exploration in Chemical Space
Alexius Wadell, Anoushka Bhutani, Victor Azumah +26
Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches…
LaDCast: A Latent Diffusion Model for Medium-Range Ensemble Weather Forecasting
Yilin Zhuang, Karthik Duraisamy
Accurate probabilistic weather forecasting demands both high accuracy and efficient uncertainty quantification, challenges that overburden both ensemble numerical weather predictio…
Active Inference AI Systems for Scientific Discovery
Karthik Duraisamy
The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine sci…
Data-driven Koopman Operator-based Prediction and Control Using Model Averaging
Daisuke Uchida, Karthik Duraisamy
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and con…
Model Predictive Control of Nonlinear Dynamics Using Online Adaptive Koopman Operators
Daisuke Uchida, Karthik Duraisamy
This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the con…
Deterministic and Probabilistic Rounding Error Analysis for Mixed-Precision Arithmetic on Modern Computing Units
Sahil Bhola, Karthik Duraisamy
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput…
Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations
Yilin Zhuang, Sibo Cheng, Karthik Duraisamy
Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of…
Stochastic Wavevector Model for Rapidly-Distorted Compressible Turbulence
Noah Zambrano, Karthik Duraisamy
A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible partic…
Finite Sample Analysis and Bounds of Generalization Error of Gradient Descent in In-Context Linear Regression
Karthik Duraisamy
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the mod…
A new dynamic slip approach for wall-modeled Large Eddy Simulations in a Consistent Discontinuous Galerkin Framework
Pratikkumar Raje, Karthik Duraisamy
A wall-modeled large eddy simulation approach is proposed in a Discontinuous Galerkin (DG) setting, building on the slip-wall concept of Bae et al. (JFM'19) and the universal scali…
Variational Bayesian Optimal Experimental Design with Normalizing Flows
Jiayuan Dong, Christian Jacobsen, Mehdi Khalloufi +4
Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte C…
Bias- and Variance-Aware Probabilistic Rounding Error Analysis for Floating-Point Arithmetic
Sahil Bhola, Karthik Duraisamy
Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often lea…
Enhancing Dynamical System Modeling through Interpretable Machine Learning Augmentations: A Case Study in Cathodic Electrophoretic Deposition
Christian Jacobsen, Jiayuan Dong, Mehdi Khalloufi +4
We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demon…