Mark A. Asch

This is my homepage and the companion website for A Toolbox for Digital Twins: from Model-based to Data-driven. SIAM (2022). This book provides a unique resource for all the modeling and computational tools needed to formulate, test and deploy Digital Twins. All the codes from the book examples are available. They can also be obtained directly from my GitHub repository. Typos and other errors are inevitable, so please help by filling in the Errata/Feedback form. Your feedback is precious. The current list of errata can be found here.

Here is a preview of the book’s cover.

My career has covered a lot of ground: from academia to industry, passing through governmental, European and international institutions. Learning from all of these, has provided a broad persepctive of how and what mathematics can propose to society. For more details, please consult my homepage and recent CV.

Publications related to the subject of Digital Twins can be found on the publications page. My previous book remains a good source for a detailed presentation of Data Assimilation.

I provide consulting and training for all aspects of Digital Twins and their implementations. Please see the dedicated pages.

In the twins section, a number of models are show-cased and an updated list of twins, with links, is provided.

Please consult regularly the blog section, where you will find updates, timely and additional material, as well as invited posts written by eminent colleagues.

Links to my social media connections are available in the page-bottom menu.

selected publications

PhysRev

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

A. Einstein^*†, B. Podolsky^*, and N. Rosen^*

Phys. Rev., New Jersey. More Information can be found here , May 1935

Abs DOI HTML PDF Video

In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.