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585 papers
Energy decomposition by potential level
Nicolas Bouleau
In the first part we study excessive functions for a Markov process that are continuous semimartingales along the sample paths. The property then follows from the theory of local t…
Generalize cross-ratios in n-dimensional Plane-Based Geometric Algebra
Enzo Harquin, Stephane Breuils, Pascal Monasse +2
We develop a complete theory of projective cross-ratios in n-dimensional Plane-Based Geometric Algebra (PGA), R(n,0,1), covering geometric objects of every grade: finite and ideal…
Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder
Kewei Zhu, Yanze Xin, Jinwei Hu +3
Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing…
Adding Decision Problem Makes Information More Valuable
Michel de Lara
We consider decision-making under incomplete information about an unknown state of nature. We show that a decision problem yields a higher value of information than another, unifor…
Exponential stability of the linearized viscous Saint-Venant equations using a quadratic Lyapunov function
Amaury Hayat, Nathan Lichtlé
In this work, we investigate the exponential stability of the viscous Saint-Venant equations by adding to the standard hyperbolic Saint-Venant equations a viscosity term coming fro…
Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis
Dong Li, Shuai Huang, Yapeng Cao +3
This study develops a Lagged Backward-Compatible Physics-Informed Neural Network (LBC-PINN) for simulating and inverting one-dimensional unsaturated soil consolidation under long-t…