And here’s what it looks like to formally prove (from the axioms of mathematics!) that the kinematic equations follow from calculus-based definitions of motion. A neat finding: change the type of “time” from real to complex, and ¾ kinematic equations hold. (6/⚛️)
We also show how these features of Lean can be used to define, prove, and interoperate *scientific* concepts. We formally define “thermodynamic system” and “ideal gas” using Lean structures, then prove that several gas laws are satisfied by the ideal gas. (5/⚛️)
Our fanciest proof is BET adsorption theory, which invokes infinite geometric series. In Lean, theorems and proof tactics can be imported from the mathlib database, which has >100k formally proved theorems, all of which are proved from the fundamental axioms of math. (3/⚛️)
Here’s what it looks like to translate Langmuir’s adsorption theory into a machine-verified math proof. The premises must be spelled out precisely, and Lean catches all the mathematical edge cases (can’t divide by zero, so need to add extra constraints to our premises). (2/⚛️)
Our first manuscript from the ATOMS Lab! "Formalizing Chemical Theory using the Lean Theorem Prover." As mathematicians use theorem provers to formally verify math proofs, we can do the same for theories in the chemical sciences. https://t.co/QeHyje7RSG (1/⚛️)
Congratulations @RodAndre160038 on completing your REU project on modeling 1,4-dioxane adsorption. Thank you for your hard work and we are glad to have you on the team this summer!
Oh my goodness, just delighted that we got our first grant! "Simulation methods for competitive adsorption in Brønsted acidic zeolites" Thank you, @NSF! https://t.co/ht2EPZQGt0 @UMBC_CBEE@ATOMSresearch
Meta-learning interatomic potentials: using an accurate #ML model to train another, much faster one, for accelerated #compchem simulations. Very excited to share this preprint describing work by @JoeMorrow3594, now available on @arxiv (https://t.co/kZRnzDHrRJ)! (1/4)
Excited to be at #AIChEAnnual!
Tomorrow, my student @Fran_Nacion presents a poster "Generating Adsorption Equations Using Symbolic Regression" from 10:00-12:30 https://t.co/mm1Gt0A6cb
I am honored to have presented my first poster at the Annual American Institute of Chemical Engineers Student Conference. I couldn’t ask for a better mentor Dr. Tyler Josephson and a more supportive @UMBC_CBEE department! @umbcAIChE@ChEnected@trjosephson#AICHE2021