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Beyond Loss Guidance: Using PDE Residuals as Spectral Attention in Diffusion Neural Operators

Sawhney, Medha, Neog, Abhilash, Khurana, Mridul, Karpatne, Anuj

arXiv.org Machine Learning

Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization instabilities and are unable to dynamically adapt their inference scheme in the presence of noisy PDE residuals. To address these limitations, we introduce PRISMA (PDE Residual Informed Spectral Modulation with Attention), a conditional diffusion neural operator that embeds PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain, enabling gradient-descent free inference. We show that PRISMA has competitive accuracy, at substantially lower inference costs, compared to previous methods across five benchmark PDEs especially with noisy observations, while using 10x to 100x fewer denoising steps, leading to 15x to 250x faster inference. Given the ubiquitous presence of partial differential equations (PDEs) in almost every scientific discipline, there is a rapidly growing literature on using neural networks for solving PDEs (Raissi et al., 2019a; Lu et al., 2019). This includes seminal works in operator learning methods such as the Fourier Neural Operator (FNO) Li et al. (2020) that learns resolution-independent mappings between function spaces of input parameters a and solution fields u. However, a major limitation of these methods is their reliance on complete and clean observations of either a or u, a condition rarely met in real-world applications where data is inherently noisy and sparse. The rise of generative models has inspired another class of methods for solving PDEs by modeling the joint distribution of a and u using diffusion-based backbones (Huang et al., 2024; Y ao et al., 2025; Lim et al., 2023; Shu et al., 2023; Bastek et al., 2024; Jacobsen et al., 2025). These methods offer two key advantages over operator learning methods: (i) they generate full posterior distributions of a and/or u, enabling principled uncertainty quantification crucial for ill-posed inverse problems, and (ii) they naturally accommodate sparse observations during inference using likelihood-based and PDE residual-based loss guidance, termed diffusion posterior sampling or test-time optimization.


Detecting Methane Plumes using PRISMA: Deep Learning Model and Data Augmentation

Groshenry, Alexis, Giron, Clement, Lauvaux, Thomas, d'Aspremont, Alexandre, Ehret, Thibaud

arXiv.org Artificial Intelligence

The new generation of hyperspectral imagers, such as PRISMA, has improved significantly our detection capability of methane (CH4) plumes from space at high spatial resolution (30m). We present here a complete framework to identify CH4 plumes using images from the PRISMA satellite mission and a deep learning model able to detect plumes over large areas. To compensate for the relative scarcity of PRISMA images, we trained our model by transposing high resolution plumes from Sentinel-2 to PRISMA. Our methodology thus avoids computationally expensive synthetic plume generation from Large Eddy Simulations by generating a broad and realistic training database, and paves the way for large-scale detection of methane plumes using future hyperspectral sensors (EnMAP, EMIT, CarbonMapper).


How AI Is Changing the Role of the Designer

#artificialintelligence

The Grid), which promise convenience: machines doing everything with algorithms that take shapes, colors, and text into design consideration. But as we saw with The Grid, these promises of the future are still very much a work in progress. So, even if AI feels a bit threatening to some design professionals, there's still quite a lot of improvement that needs to happen before AI becomes a true threat. "At its heart, AI is computer programming that learns and adapts. It can't solve every problem, but its potential to improve our lives is profound."


AI Masterpieces: But is it Art?

#artificialintelligence

It's said that all that needs to happen for something to be considered art is for someone who identifies as an artist to declare it as such. But to most of us, art is created, not just declared and should be delivered with a healthy dose of creative human agency. Regardless of definitions, most of us know art when we see it, don't we? And what does it matter in any case? The short answer is that computer art has been challenging us to confront these questions for over 50 years--the role of the artist (and that of the machine) in the field of computer art has never been completely easy to resolve.


Prisma hopes to market its AI photo filtering tech

Engadget

Prisma's machine learning photography app may not be as hot as it was in 2016, but that doesn't mean it's going away. If the developer has its way, you'll see its technology in many places before long. The company tells The Verge that it's shifting its focus from just its in-house app to marketing numerous computer vision tools based on its AI technology, ranging from object recognition to face mapping and detecting the foreground in an image. In theory, you'd see Prisma's clever processing find its way into your next phone or a favorite social photography app. The Prisma app is staying put, to be clear -- it has 5 million to 10 million monthly users, which is no mean feat for a small startup. It just won't be the sole focus.


Flipboard on Flipboard

#artificialintelligence

The startup behind the Prisma style transfer app is shifting focus onto the b2b space, building tools for developers that draw on its expertise using neural networks and deep learning technology to power visual effects on mobile devices. It's launched a new website, Prismalabs.ai, detailing this new offering. Initially, say Prisma's co-founders, they'll be offering an SDK for developers wanting to add effects like style transfer and selfie lenses to their own apps -- likely launching an API mid next week. Then, in the "next month or so", they also plan to offer another service for developers wanting help to port their code to mobile. This was, after all, how the co-founders originally came up with the idea for the Prisma app -- having seen a style transfer effect working (slowly) on a desktop computer and realized how much potential it would have if it could be made to work in near real-time on mobile.


Prisma shifts focus to b2b with an API for AI-powered mobile effects

#artificialintelligence

Initially, say Prisma's co-founders, they'll be offering an SDK for developers wanting to add effects like style transfer and selfie lenses to their own apps -- likely launching an API mid next week. The wave of augmented reality apps that are coming down the smartphone pipe, driven by more powerful hardware and active encouragement from mobile platforms, could also help generate demand for Prisma's effects, reckons Moiseenkov, as they can offer object tracking as well as face tracking via APIs or an SDK. "We want to explore the CV [computer vision] area and help companies also produce a greater user experience with AI -- helping people to communicate easier, to solve their tasks," adds Moiseenkov. The app achieved its effects not by applying filters to the photo but by utilizing neural networks and deep learning to process the original photo in the chosen style -- generating a new image that combined both input sources.


Prisma shifts focus to b2b with an API for AI-powered mobile effects

#artificialintelligence

The startup behind the Prisma style transfer app is shifting focus onto the b2b space, building tools for developers that draw on its expertise using neural networks and deep learning technology to power visual effects on mobile devices. It's launched a new website, Prismalabs.ai, detailing this new offering. Initially, say Prisma's co-founders, they'll be offering an SDK for developers wanting to add effects like style transfer and selfie lenses to their own apps -- likely launching an API mid next week. Then, in the "next month or so", they also plan to offer another service for developers wanting help to port their code to mobile. This was, after all, how the co-founders originally came up with the idea for the Prisma app -- having seen a style transfer effect working (slowly) on a desktop computer and realized how much potential it would have if it could be made to work in near real-time on mobile.


Google acquires AIMatter, maker of the Fabby computer vision app

#artificialintelligence

The search and Android giant has acquired AIMatter, a startup founded in Belarus that has built both a neural network-based AI platform and SDK to detect and process images quickly on mobile devices, and a photo and video editing app that has served as a proof-of-concept of the tech called Fabby. We'd had wind of the deal going down as far back as May, although it only officially closed today. Fabby and Google have confirmed the deal to us and there should be a statement posted on AIMatter's site about the news soon (update: it's up). A Google spokesperson provided TC with a short statement: "We are excited to welcome the AIMatter team to Google." Terms of the sale are not being disclosed, but we understand that Fabby -- which has had over 2 million downloads -- will continue to run, and from what we understand most of AIMatter's employees will come over to Google.


Welcome To The Future Of Marketing: The A.I. Based Design

#artificialintelligence

Many people believed that modern technology will first replace the low wage jobs from the industries that are dependent on manual labor rather than intellectual work. However, the latest innovations in robotics and A.I. tend to contradict our previous beliefs: we are now entering a new era, of A.I. based design that hopefully, will change everything for the best. Until recently, computer generated design was regarded more as a sci-fi idea rather than a reality. The development of artificial intelligence was focused on other goals and nobody could have dreamed about it being capable of actually delivering something useful to mankind. Sure, we all have at least once admired beautiful fractals generated by computers but let's face it, they were not actually visual designs.