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High-power lasers are vital for particle acceleration, imaging, fusion and materials processing, requiring precise control and high-energy delivery. Laser plasma accelerators (LPAs) demand laser positional stability at focus to ensure consistent electron beams in applications such as X-ray free-electron lasers and high-energy colliders. Achieving this stability is especially challenging for the low-repetition-rate lasers in current LPAs. We present a machine learning method that predicts and corrects laser pointing instabilities in real-time using a high-frequency pilot beam. By preemptively adjusting a correction mirror, this approach overcomes traditional feedback limits. Demonstrated on the BELLA petawatt laser operating at the terawatt level (30 mJ amplification), our method achieved root mean square pointing stabilization of 0.34 and 0.59 
$\unicode{x3bc} \mathrm{rad}$ in the x and y directions, reducing jitter by 65% and 47%, respectively. This is the first successful application of predictive control for shot-to-shot stabilization in low-repetition-rate laser systems, paving the way for full-energy petawatt lasers and transformative advances across science, industry and security.
$ {\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$
In [2], Beilinson–Lusztig–MacPherson (BLM) gave a beautiful realization for quantum 
$\mathfrak {gl}_n$ via a geometric setting of quantum Schur algebras. We introduce the notion of affine Schur superalgebras and use them as a bridge to link the structure and representations of the universal enveloping superalgebra 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ of the loop algebra 
$\widehat {\mathfrak {gl}}_{m|n}$ of 
${\mathfrak {gl}}_{m|n}$ with those of affine symmetric groups 
${\widehat {{\mathfrak S}}_{r}}$. Then, we give a BLM type realization of 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ via affine Schur superalgebras.
The first application of the realization of 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ is to determine the action of 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ on tensor spaces of the natural representation of 
$\widehat {\mathfrak {gl}}_{m|n}$. These results in epimorphisms from 
$\;{\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ to affine Schur superalgebras so that the bridging relation between representations of 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ and 
${\widehat {{\mathfrak S}}_{r}}$ is established. As a second application, we construct a Kostant type 
$\mathbb Z$-form for 
${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ whose images under the epimorphisms above are exactly the integral affine Schur superalgebras. In this way, we obtain essentially the super affine Schur–Weyl duality in arbitrary characteristics.
