10 papers · 1 filter
MiNO: Cotangent-bundle propagator learning for PDEs
Gnankan Landry Regis N'guessan, Bum Jun Kim
Scientific machine learning for partial differential equations commonly targets solution fields, as in physics-informed neural networks, or solution maps, as in neural operators. W…
SEAM: Global consistency beyond local accuracy in scientific machine learning
Gnankan Landry Regis N'guessan, Bum Jun Kim
Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction. Yet such local checks cannot establish w…
EqOD: Symmetry-Informed Stability Selection for PDE Identification
Gnankan Landry Regis N'guessan, Bum Jun Kim
Data-driven identification of partial differential equations (PDEs) relies on sparse regression over a candidate library of differential operators, where larger libraries inflate f…
Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
Bum Jun Kim, Gnankan Landry Regis N'guessan
Physics-informed neural networks (PINNs) train a single neural approximation by minimizing multiple physics- and data-derived losses, but the gradients of these losses often interf…
FI-KAN: Fractal Interpolation Kolmogorov-Arnold Networks
Gnankan Landry Regis N'guessan
Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal…
Radial Müntz-Szász Networks: Neural Architectures with Learnable Power Bases for Multidimensional Singularities
Gnankan Landry Regis N'guessan, Bum Jun Kim
Radial singular fields, such as , , and crack-tip profiles, are difficult to model with current coordinate-separable neural architectures. We formally establish this r…
Discovering Scaling Exponents with Physics-Informed Müntz-Szász Networks
Gnankan Landry Regis N'guessan, Bum Jun Kim
Physical systems near singularities, interfaces, and critical points exhibit power-law scaling, yet standard neural networks leave the governing exponents implicit. We introduce ph…
Müntz-Szász Networks: Neural Architectures with Learnable Power-Law Bases
Gnankan Landry Regis N'guessan
Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power b…
v-PuNNs: van der Put Neural Networks for Transparent Ultrametric Representation Learning
Gnankan Landry Regis N'guessan
Conventional deep learning models embed data in Euclidean space , a poor fit for strictly hierarchical objects such as taxa, word senses, or file systems. We introduc…
Localized Weather Prediction Using Kolmogorov-Arnold Network-Based Models and Deep RNNs
Ange-Clement Akazan, Verlon Roel Mbingui, Gnankan Landry Regis N'guessan +1
Weather forecasting is crucial for managing risks and economic planning, particularly in tropical Africa, where extreme events severely impact livelihoods. Yet, existing forecastin…