This paper establishes a connection between non-convex optimization and nonlinear partial differential equations (PDEs). We interpret empirically successful relaxation techniques motivated from ...

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University of Utah engineers encode partial differential equations in light and feed them into newly designed optical neural engine, or ONE, to accelerate machine learning.

Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

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Researchers have found a new way to solve high-degree polynomial equations, previously thought impossible for 200 years. This math breakthrough reopens algebra.

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ABSTRACT: In previous papers, we proposed the important Z transformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time.

Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

All the latest science news on partial differential equations from Phys.org. Find the latest news, advancements, and breakthroughs.