April Tran, Department of Applied Mathematics, University of Colorado Boulder

WLaSDI: Weak-form Latent Space Dynamics Identification

In the field of computational biology, the utilization of data to facilitate fast and accurate physical simulations has emerged as an important domain with wide-ranging applications. We introduce a parametric data-driven procedure called WLaSDI: Weak-form Latent Space Dynamics Identification, an extension of LaSDI: Latent Space Dynamics Identification. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. Similar to LaSDI, WLaSDI first compresses data, then acquires the local latent space models and employs two interaction methods: Interpolated point-wise and region-based. With WLaSDI, the local latent space is obtained using WENDy (Weak-form Estimation of Nonlinear Dynamics). Compared to the standard SINDy used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a robust and accurate simulation. The applicability of WLaSDI extends beyond the field of computational biology and can be effectively employed in a wide range of scenarios, even those outside the domain of biology. To demonstrate its versatility and effectiveness, we conducted tests of WLaSDI on various mathematical models, including the Fisher equation, Burgers equation, Heat conduction, and Radial Advection.

April Tran, Department of Applied Mathematics, University of Colorado Boulder

WLaSDI: Weak-form Latent Space Dynamics Identification

In the field of computational biology, the utilization of data to facilitate fast and accurate physical simulations has emerged as an important domain with wide-ranging applications. We introduce a parametric data-driven procedure called WLaSDI: Weak-form Latent Space Dynamics Identification, an extension of LaSDI: Latent Space Dynamics Identification. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. Similar to LaSDI, WLaSDI first compresses data, then acquires the local latent space models and employs two interaction methods: Interpolated point-wise and region-based. With WLaSDI, the local latent space is obtained using WENDy (Weak-form Estimation of Nonlinear Dynamics). Compared to the standard SINDy used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a robust and accurate simulation. The applicability of WLaSDI extends beyond the field of computational biology and can be effectively employed in a wide range of scenarios, even those outside the domain of biology. To demonstrate its versatility and effectiveness, we conducted tests of WLaSDI on various mathematical models, including the Fisher equation, Burgers equation, Heat conduction, and Radial Advection.