Kent-Andre Mardal
Chief Research Scientist,
Simula Research Laboratory
e-mail: kent-and@simula.no
Professor in Mechanics,
Department of Mathematics,
University of Oslo
e-mail: kent-and@math.uio.no
Researcher at
K.G. Jebsen Center for Brain Fluid Research
Consulant for
Expert Analytics
e-mail: kent@xal.no
Yo, we diving deep in the machine learnin' scene, A priori, a posteriori, PINNs in between. Physics-informed neural networks, chasing errors in flight, Linear PDEs, breaking codes, taking it to new heights. Elliptic equations, primal, mixed, it's a feast, Elasticity, parabolic, hyperbolic, never least. Stokes equations, kicking in, making waves, Constrained optimization, in the PDE caves. Abstract framework, in bilinear forms we converse, Coercivity, continuity, errors we disperse. Insights into neural nets, high-dimension PDEs in sight, Constraints in the ansatz class, taking flight. Beside the Poisson, estimates take the stage, Best-approximation, a posteriori, setting the rage. In the PINN realm, pioneers we stand, Controlling errors, in the ML land. Recent advances, PINN optimization on display, Numerical examples, accuracy leading the way. In the rhythm of solutions, we groove, PINN rap, accuracy we prove.ChatGPT poem version of paper (ack Rami)
And also NRK and P1 .
reported on our findings here
