12 papers
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…
PALMA: A Lightweight Tropical Algebra Library for ARM-Based Embedded Systems
Gnankan Landry Regis N'guessan
Tropical algebra, including max-plus, min-plus, and related idempotent semirings, provides a unifying framework in which many optimization problems that are nonlinear in classical…
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…
The Reflexive Integrated Information Unit: A Differentiable Primitive for Artificial Consciousness
Gnankan Landry Regis N'guessan, Issa Karambal
Research on artificial consciousness lacks the equivalent of the perceptron: a small, trainable module that can be copied, benchmarked, and iteratively improved. We introduce the R…
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…