12 papers
Stochastic Lanczos Quadrature for Computational Uncertainty in Linear Algebra
Hassan Fifen, Issa Karambal, Philipp Hennig
Applying a matrix function to a vector is a common operation in large-scale scientific computing, such as Bayesian inference. When the matrix is symmetric positive definite and the…
ReliableNet: A Chance-Constrained Approach to Trustworthy Classification in Deep Learning
Ange-Clément Akazan, Ineza Remy Mugenga, Abebe Geletu +2
A prediction that is both confident and wrong is a critical reliability failure because it can bypass abstention and human review precisely when the model is mistaken. Empirical ri…
A Range-Deflated Stochastic Lanczos Quadrature Method for Large-Scale Log-Determinant Estimation
Verlon Roel Mbingui, Antoine Tambue, Issa Karambal
Estimating the logarithm of the determinant of large sparse symmetric positive definite matrices is an important problem in numerical linear algebra, machine learning, Gaussian pro…
Novel technique based on Léja Points Approximation for Log-determinant Estimation of Large matrices
Verlon Roel Mbingui, Antoine Tambue, Issa Karambal
The computation of the Log-determinant of large, sparse, symmetric positive definite (SPD) matrices is essential in many scientific computational fields such as numerical linear al…
Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
Brenda Anague, Bamdad Hosseini, Issa Karambal +1
Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neur…
RRaPINNs: Residual Risk-Aware Physics Informed Neural Networks
Ange-Clément Akazan, Issa Karambal, Jean Medard Ngnotchouye +1
Physics-informed neural networks (PINNs) typically minimize average residuals, which can conceal large, localized errors. We propose Residual Risk-Aware Physics-Informed Neural Net…
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…
AI and the Future of Work in Africa White Paper
Jacki O'Neill, Vukosi Marivate, Barbara Glover +71
This white paper is the output of a multidisciplinary workshop in Nairobi (Nov 2023). Led by a cross-organisational team including Microsoft Research, NEPAD, Lelapa AI, and Univers…
A physics-informed neural network framework for modeling obstacle-related equations
Hamid El Bahja, Jan Christian Hauffen, Peter Jung +2
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current…
Numerical evaluation of operator determinants
Issa Karambal
For any integral operator in the Schatten--von Neumann classes of compact operators and its approximated operator obtained by using for example a quadrature or…
Evans function and Fredholm determinants
Issa Karambal, Simon J. A Malham
We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line.…