We present the Digital Math framework as the foundation for modern science based on constructive digital mathematical computation. The computed result (coefficient vector, FEM function, plot, etc.) is a mathematical theorem, and the mathematical Open Source code, here in the FEniCS framework, and computation is the mathematical proof. We can also derive additional constructive proofs from the FEniCS and FEM formulation, such as stability.
Based on the Digital Math framework and the FEniCS realization, we present our Direct FEM Simulation (DFS) methodology together with predictions of the most advanced benchmarks available, unlocking the grand challenge of turbulence and aerodynamics.
Digital Math represents digitalization of mathematics, society, industry and society in the form of automated and easily understandable computation of mathematical models in the Open Source FEniCS framework with world-leading performance and recognized at the highest level of science and industry together with an effective pedagogical concept with combined abstract theory and mathematical interactive programming in a cloud-HPC web-interface.
With our computational framework you can predict and understand the grand challenges of science and technology.
May 14, 2019
The report “Reproducibility and Replicability in Science” by the US National Academies of Sciences, Engineering and Medicine is just out, it’s of key importance for our scientific work. Here’s an article on the report, and the report itself:
Lorena Barba is a prominent US scientist, driving forward several Open Source initiatives such as NumFOCUS, and one of the authors of the report.
Here’s a quote from the article:
””” Barba told Physics World. “What we are calling for is changing those norms to give importance to the full set of digital objects that are part of a scientific study and acknowledging that the scientific paper is insufficient today in its methods section to include all of the information needed for another researcher to confirm the results or build from those results.” “””
What Lorena is saying is that if a scientific paper is not reproducible, then it cannot really be considered a scientific publication. Here’s another article on this:
This is also mirrored in the Swedish guidelines for Open Access in Science:
There is a crisis of reproducibility in science today:
One of the most cited papers in recent years is the paper “Why most published research findings are false”:
The Digital Math framework as the foundation for modern science based on constructive digital mathematical computation, is a solution to the crisis. The computed result (coefficient vector, FEM function, plot, etc.) is a mathematical theorem, and the mathematical Open Source code, here in the FEniCS framework, and computation is the mathematical proof.
Based on the Digital Math framework and the Unicorn/FEniCS realization, we present our Direct FEM Simulation (DFS) methodology together with predictions of the most advanced benchmarks available, unlocking the grand challenge of turbulence and aerodybamics.