116 citations · 193 across the 15 of their papers we have counts for
18 papers
Data-Driven, ML-assisted Approaches to Problem Well-Posedness
Tom Bertalan, George A. Kevrekidis, Eleni D Koronaki +3
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. We…
Data-driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactors
Tianqi Cui, Tom S. Bertalan, Nelson Ndahiro +4
Fed-batch culture is an established operation mode for the production of biologics using mammalian cell cultures. Quantitative modeling integrates both kinetics for some key reacti…
Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information
Saurabh Malani, Tom S. Bertalan, Tianqi Cui +3
Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform t between successive measurements); and at a specific time poi…
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
Aiqing Zhu, Tom Bertalan, Beibei Zhu +2
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of t…
Certified Invertibility in Neural Networks via Mixed-Integer Programming
Tianqi Cui, Thomas Bertalan, George J. Pappas +3
Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there…
Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning
Felix Dietrich, Alexei Makeev, George Kevrekidis +4
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surr…