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๐ผ๐ฃ Katฤฑlฤฑm Mart 2024
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Discovering governing equations from a handful of sensors
Modeling turbulent flows, climate fields, or physical systems captured on video is hard: the data are high-dimensional, noisy, and partially observed. Deep learning surrogates help but are unstable on long rollouts, data-hungry, and opaque.
Mars Liyao Gao and coauthors propose SINDy-SHRED, a lightweight architecture that jointly solves sensing, model reduction, and equation discovery. A Gated Recurrent Unit processes the time history of a few sparse sensors and maps it into a low-dimensional latent state, while a shallow decoder reconstructs the full field from that state. A regularization term forces the latent dynamics into the SINDy class: sparse combinations of polynomials and trigonometric terms. Restricting the library to linear terms gives Koopman-SHRED.
The results span several benchmarks. Twenty-seven years of NOAA sea-surface temperature data are captured by a 3D linear ODE that recovers the annual cycle and a slow warming mode. Flow over a cylinder, learned from video with only 0.05% of the pixels as sensors, yields both a nonlinear limit cycle and a linear Koopman model, both new to a problem studied for decades. A pendulum video exposes nonlinear damping beyond the usual linear assumption, and isotropic turbulence is compressed to eight oscillatory latent modes.
On pendulum video prediction, SINDy-SHRED beats ConvLSTM, PredRNN, ResNet, and SimVP with only 44K parameters (versus 2.7M for ResNet) and 17 minutes of training on a single GPU. The loss landscape is empirically convex across every tested dataset, which is unheard of in deep learning, and the authors prove explicit error bounds for long-horizon prediction.
For materials development, energy research, biotech, or process industries, this reframes what is feasible with limited instrumentation. A few well-placed probes can yield interpretable governing equations usable for long-term prediction, control, and digital twins, without dense sensor grids or costly high-fidelity simulations. The symbolic output is also easier to audit in regulated settings than a black-box surrogate.
Paper: Gao et al., PNAS (2026) โ CC BY 4.0 | doi.org/10.1073/pnas.2โฆ

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genuinely how it feels trying to just peacefully exist in public as a 6โ1 goddess
Umay@benumayim
Diลisini gรถren bir kertenkelenin tepkisi :
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