Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable answer specific scientific questions. In this Perspective, we explore differentiable as a pathway dissolve the perceived barrier between proce...

Invariants that incrementally maintain the value of expressions under assignments to their variables are a natural abstraction to build high-level local search algorithms. But their functionalities are not sufficient to allow arbitrary expressions as constraints or objective functions as in constraint programming. Differentiable invariants bridge this expressiveness gap. A differentiable invari...

A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers $vn%n50 ` to represent the ‘‘entropic moments’’ * [0,a]@r(x)# dx of an unknown non-negative, decreasing and differentiable ~a.e.! density function r(x) with a finite interval support. These moments are called entropic moments because they are closely conne...

∆u = ∂2u ∂x1 + ∂2u ∂x2 where x = (x1, x2) ∈ R2 are Cartesian coordinates. Even though the Poisson equation looks very special it is an important model case representing several problems from physics and engineering, e.g. electrostatics, stationary heat transfer and other diffusion problems. Variations of the techniques we will study apply to a wide class of second order so-called elliptic probl...