Tootfinder

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space
Xinyue Yu, Hayden Schaeffer
https://arxiv.org/abs/2512.17884 https://arxiv.org/pdf/2512.17884 https://arxiv.org/html/2512.17884
arXiv:2512.17884v1 Announce Type: new
Abstract: Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically justified approximations that require less training than standard methods. However, they can become computationally prohibitive for large training sets and can be sensitive to noise. We propose a regularized random Fourier feature (RRFF) approach, coupled with a finite element reconstruction map (RRFF-FEM), for learning operators from noisy data. The method uses random features drawn from multivariate Student's $t$ distributions, together with frequency-weighted Tikhonov regularization that suppresses high-frequency noise. We establish high-probability bounds on the extreme singular values of the associated random feature matrix and show that when the number of features $N$ scales like $m \log m$ with the number of training samples $m$, the system is well-conditioned, which yields estimation and generalization guarantees. Detailed numerical experiments on benchmark PDE problems, including advection, Burgers', Darcy flow, Helmholtz, Navier-Stokes, and structural mechanics, demonstrate that RRFF and RRFF-FEM are robust to noise and achieve improved performance with reduced training time compared to the unregularized random feature model, while maintaining competitive accuracy relative to kernel and neural operator tests.
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"Literaturrecherche mit KI – Scholar Labs" https://www.profi-wissen.de/literaturrecherche-mit-ki-scholar-labs/

"Nearly three-quarters of western US overdue for wildfires, research indicates"
#US #USA #America #Wildfires

Nearly three-quarters of western US overdue for wildfires, research indicates
Wildfires can benefit forests by clearing old debris, leaving behind fertilizer, and more. For over a century, the United States has poured billions of dollars into fire suppression tactics to keep people, homes and critical environments safe, but suppression can deprive landscapes of necessary burns and increase potential fuel for large fires in the future.

Im April spreche ich auf der Rack&Stack Konferenz über Decomputing. Weitere Teile des Programms sind nun öffentlich.
(Original title: Golem-Konferenz Rack & Stack 2026: Diese Speaker stehen fest, jetzt verbilligte Tickets sichern)
https://www.…

Golem-Konferenz Rack & Stack 2026: Diese Speaker stehen fest, jetzt verbilligte Tickets sichern - Golem.de
Das Programm für die Rack & Stack steht in großen Teilen, wir haben Zusagen von einigen tollen Speakern! Bis Ende Januar können noch Vorschläge eingereicht und vergünstigte Tickets gekauft werden.

Cowboys' Jerry Jones says he's 'sad' for Micah Parsons after Packers star pass rusher suffers torn ACL

https://www.cbssports.com/nfl/news/cowboys-jerry-jones-mic…

Der Friedenspreis der Unternehmensgruppe Theo Müller ist ihm damit sicher!
https://www.n-tv.de/mediathek/videos/politik/Skurriler-Termin-Trump-beendet-Krieg-gegen-Vollmilch-id30243787.html

"Er ist ein Friedenspräsident": Skurriler Termin: Trump beendet "Krieg" gegen Vollmilch
Inmitten der vulnerablen politischen Weltlage lädt Trump zu einem ungewöhnlichen Pressetermin. Das Thema: Vollmilch. Diese wird nach Einschränkungen wegen des hohen Fettgehalts an Schulen zurückkehren. Der Gesundheitsminister lobt Trump für seine Befriedung des "Kriegs gegen ungesättigtes Fett".

Study: ~200 Instacart shoppers in four US cities were shown different prices for the same 20 grocery items; Instacart confirms it is running short term "tests" (Ben Casselman/New York Times)
https://www.nytimes.com/2025/12/09/business/instacart-algori…

Same Product, Same Store, but on Instacart, Prices Might Differ
The findings are the latest example of how the notion of a single price is breaking down in the digital age, a trend economists say could be pushing up some prices.

One baby Jesus lies in a manger in the snow, wrapped in a silver emergency blanket with his wrists zip-tied.
Mary stands nearby outside the Lake Street Church in Evanston, Illinois, wearing a plastic gas mask and flanked by Roman soldiers in tactical vests labeled “ICE.”
In another Chicago suburb, not far from an Immigration and Customs Enforcement facility that has drawn protests over detentions, a sign at the manger outside the Urban Village Church says
“Due to ICE activit…

Church nativity displays on immigration draw praise, outrage in Illinois and Massachusetts
Nativity scenes at some churches are sparking fierce debates. At Lake Street Church in Evanston, Illinois, the baby Jesus lies with zip-tied wrists in the kind of emergency blankets given ICE detainees. At St. Susanna Parish in Dedham, Massachusetts, the manger sits empty, beneath a sign reading “ICE was here.” Supporters say Jesus, Mary and Joseph were refugees, comparing them to immigrant communities facing federal raids. Critics call the displays political and sacrilegious. The controver…

heise | GitHub Spark im Test: Apps programmieren, ohne eine Zeile Code zu schreiben
Prompt eingeben, Enter drücken und fertig ist die App – ohne eine Zeile Code zu tippen. Wir haben getestet, was GitHubs KI-Programmierer Spark wirklich kann.

As one might expect El Cheato appointed judges rule in favor of trump far more often than do judges appointed by prior presidents.
But the amount of that imbalance is beyond astounding.
From the NY Times:
"Trump’s ‘Superstar’ Appellate Judges Have Voted 133 to 12 in His Favor"
Which causes me to repeat my suggestions, from year 2020, about how we can remove power from those judges by using a technique well practiced elsewhere - redefining jobs and "rubb…