Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in differentiable fashion but have difficulties handling topology changes. Implicit signed-distance functions, on other hand, offer better support changes much more difficult use physics-based rendering. We introduce new pipe...

Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that backpropagation, which computes the exact gradient any output program with respect to input. This achieved efficiently within differentiable programming paradigm, utilizes automatic differentiation (AD) each step computer chain rule. A classic application ...

Artificial reverberation (AR) models play a central role in various audio applications. Therefore, estimating the AR model parameters (ARPs) of reference is crucial task. Although few recent deep-learning-based approaches have shown promising performance, their non-end-to-end training scheme prevents them from fully exploiting potential deep neural networks. This motivates introduction differen...

It should be evident to you that (1.5) is equivalent to (1.3). Visually, if the graph of a function f at (a, f(a)) either has no unique tangent line or has a vertical tangent line then f is not differentiable at the point a. A function that is differentiable at every point in Dom(f) is said to be differentiable. A function that is differentiable at every point in a set S ⊂ Dom(f) is said to be ...

The theory of scale relativity [14] is an attempt to study the consequences of giving up the hypothesis of space-time differentiability. One can show [14] [15] that a continuous but nondifferentiable space-time is necessarily fractal. Here the word fractal [12] is taken in a general meaning, as defining a set, object or space that shows structures at all scales, or on a wide range of scales. Mo...

functionals were discovered and used by volterra over a century ago in his study of the motions of viscous elastic materials and electromagnetic fields. the need to precisely account for the qualitative effects of the cohesion and shape of the domains of these functionals was the major impetus to the development of the branch of mathematics known as topology, and today large numbers of mathemat...