field
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A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the extra fields'' from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear forms. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the extra fields'' can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.
Multiscale Fields of Patterns
Pedro Felzenszwalb, John G. Oberlin
We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image reflect non-local properties of the original image. In the case of binary images local properties are defined by the binary patterns observed over small neighborhoods around each pixel. With the multiscale representation we capture the frequency of patterns observed at different scales of resolution. This framework leads to expressive priors that depend on a relatively small number of parameters. For inference and learning we use an MCMC method for block sampling with very large blocks. We evaluate the approach with two example applications.
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- Europe > Sweden > Östergötland County > Linköping (0.04)
- Information Technology > Artificial Intelligence > Representation & Reasoning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Undirected Networks > Markov Models (0.71)
Geometric Neural Process Fields
Yin, Wenzhe, Xiao, Zehao, Shen, Jiayi, Chen, Yunlu, Snoek, Cees G. M., Sonke, Jan-Jakob, Gavves, Efstratios
This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. To tackle this, we propose Geometric Neural Process Fields (G-NPF), a probabilistic framework for neural radiance fields that explicitly captures uncertainty. We formulate NeF generalization as a probabilistic problem, enabling direct inference of NeF function distributions from limited context observations. To incorporate structural inductive biases, we introduce a set of geometric bases that encode spatial structure and facilitate the inference of NeF function distributions. Building on these bases, we design a hierarchical latent variable model, allowing G-NPF to integrate structural information across multiple spatial levels and effectively parameterize INR functions. This hierarchical approach improves generalization to novel scenes and unseen signals. Experiments on novel-view synthesis for 3D scenes, as well as 2D image and 1D signal regression, demonstrate the effectiveness of our method in capturing uncertainty and leveraging structural information for improved generalization.
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- Information Technology > Artificial Intelligence > Vision (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning (1.00)
- Information Technology > Artificial Intelligence > Natural Language (0.93)
- Information Technology > Artificial Intelligence > Machine Learning > Neural Networks > Deep Learning (0.92)
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the "extra fields'' from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear forms. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the "extra fields'' can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.
Dylan Field 'Got a Real Kick' Out of This Week's Enron Relaunch
Figma cofounder Dylan Field is seemingly a big Enron fan--or rather, of the crypto-fueled semi-parodic relaunch of the company that hit the web earlier this week. Sporting an oversized Enron hoodie during his conversation with WIRED editor at large Steven Levy during The Big Interview event in San Francisco on Tuesday, Field said he's always been a fan of the Enron logo, which was the last one crafted by legendary American graphic designer Paul Rand, of ABC, IBM, UPS, and Westinghouse logo fame. But he said he also "got a real kick" out of the potential Enron relaunch, which has been tied to "Birds Aren't Real" creator Connor Gaydos. As someone who was just 9 years old when Enron imploded in 2001, Field says he wonders (optimistically, it seems) if it's possible to build a new company on the back of the tainted brand, given that his generation might not carry the kind of baggage related to the company's stumbles that others do. Either way, it seems, it's a question of the power of design, something Field and Levy focused on more broadly as their chat went on, talking not just about the creation and evolution of the Figma platform, but also where the cofounder sees the company going in the immediate future.
- Information Technology > Artificial Intelligence > Natural Language > Large Language Model (0.64)
- Information Technology > Artificial Intelligence > Natural Language > Chatbot (0.64)
- Information Technology > Artificial Intelligence > Machine Learning > Neural Networks > Deep Learning > Generative AI (0.64)
Deepfakes Are Being Used For Good – Here's How - Liwaiwai
In the second season of BBC mystery thriller The Capture, deepfakes threaten the future of democracy and UK national security. In a dystopia set in present day London, hackers use AI to insert these highly realistic false images and videos of people into live news broadcasts to destroy the careers of politicians. But my team's research has shown how difficult it is to create convincing deepfakes in reality. In fact, technology and creative professionals have started collaborating on solutions to help people spot bogus videos of politicians and celebrities. We stand a decent chance of staying one step ahead of fraudsters.
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Advancements In Computer Vision Models For View Synthesis: A Survey
In this post I survey a collection of Computer Vision Models that have made key advancements for View Synthesis. The fundamental idea behind View synthesis is the ability to take two-dimensional images, or videos, from different camera viewpoints and construct realistic novel views from them. Being able to synthesize a realistic novel view can depend on many factors such as, sufficient input images across various viewpoints and quality or resolution of the provided images. I will be only discussing models that have produced satisfactory results given their set of input and test images. Specifically, I have researched SRN (Scene Representation Networks), NeRF (Neural Radiance Fields), and NeuMan (Neural Human Radiance Field From a Single Video).
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The Field of Data Science Continues to Change the World for the Better - Big Data Analytics News
Sci-fi novels and television shows predicted the invention of self-driving cars, robot butlers, and self-lacing shoes, but without data science, these products would remain fiction. But data science is capable of much more than that. Data science began in the 1960s as a branch of computer science, but the term "data scientist" wasn't coined until the late 2000s. Since the 1990s, data scientists have been collecting user data, but it wasn't until the early 2010s that it was used to make sales and new technology. Applications that collect and analyze data rely on statistics and statistical models to create outcomes.
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