BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alejandro Queiruga (Google\, LLC) DTSTART:20200701T162500Z DTEND:20200701T165000Z DTSTAMP:20260423T040116Z UID:SciDL/4 DESCRIPTION:Title: Co ntinuous-in-Depth Neural Networks through Interpretation of Learned Dynami cs\nby Alejandro Queiruga (Google\, LLC) as part of Workshop on Scient ific-Driven Deep Learning (SciDL)\n\n\nAbstract\nData-driven learning of d ynamical systems is of interest to the scientific community\, which wants to recover information about the true physics from the discretized model\, and the machine learning community\, which wants to improve model interpr etability and performance. We present a refined interpretation of learned dynamical models by investigating canonical systems. Recent ML literature draws a metaphor between residual components of neural networks and a forw ard Euler time integrator\, but we show that these components actually lea rn a more accurate integrator. We examine\, the harmonic oscillator\, 1D w ave equation\, and the pendulum in two forms\, using purely linear models\ , feed-forward shallow neural networks\, and neural networks embedded in t ime integrators. Each of the model configurations overfit to a better oper ator than commonly understood\, confounding recovery of physics and attemp ts to improve the algorithms. We show two analytical methods for reconstru cting underlying operators from linear systems. For the nonlinear problems \, unmodified neural networks outperform the expected numerical methods\, but do not allow for inspection or generalization. Embedding the models in integrators such as RK4 improves performance and generalizability. Howeve r\, for the constrained pendulum\, the model is still better than excepted \, exhibiting better than expected stiffness-stability. We conclude by rev isiting the components of neural networks where improvements are suggested .\n LOCATION:https://researchseminars.org/talk/SciDL/4/ END:VEVENT END:VCALENDAR