182 citations · 218 across the 11 of their papers we have counts for
11 papers
GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms
Juan Diego Toscano, Zhaojie Chai, George Em Karniadakis
Language-model agents plan, execute, and evaluate scientific workflows. However, the problem--method relationships guiding their choices remain implicit, so plausible outputs can v…
ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
Juan Diego Toscano, Daniel T. Chen, George Em Karniadakis
Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a…
A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen +2
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these…
Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness
Lunji Song, Zilan Cheng, Juan Diego Toscano +1
We explicitly construct an approximate version of the Kolmogorov superpositions, which is composed of C2-inner and outer functions, and can approximate an arbitrary alpha Holder co…
FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design
Chenxi Wu, Juan Diego Toscano, Khemraj Shukla +7
We propose FMEnets, a physics-informed machine learning framework for the design and analysis of non-ideal plug flow reactors. FMEnets integrates the fundamental governing equation…
KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a ne…
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese +4
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and…
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
Juan Diego Toscano, Theo Käufer, Zhibo Wang +3
We propose the Artificial Intelligence Velocimetry-Thermometry (AIVT) method to infer hidden temperature fields from experimental turbulent velocity data. This physics-informed mac…
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang +2
Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning mode…
Learning in PINNs: Phase transition, diffusion equilibrium, and generalization
Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos +1
We investigate the learning dynamics of fully-connected neural networks through the lens of the neural gradient signal-to-noise ratio (SNR), examining the behavior of first-order o…
Residual-based attention in physics-informed neural networks
Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos +1
Driven by the need for more efficient and seamless integration of physical models and data, physics-informed neural networks (PINNs) have seen a surge of interest in recent years.…