Daily Papers

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction. The study presents a neural operator based on the dynamic mode decomposition algorithm (DMD), mapping functional spaces, which combines DMD and deep learning (DL) for spatiotemporal processes efficient modeling. Solving PDEs for various initial and boundary conditions requires significant computational resources. The method suggested automatically extracts key modes and system dynamics using them to construct predictions, reducing computational costs compared to traditional numerical methods. The approach has demonstrated its efficiency through comparative analysis of performance with closest analogues DeepONet and FNO in the heat equation, Laplaces equation, and Burgers equation solutions approximation, where it achieves high reconstruction accuracy.

We introduce ResPlan, a large-scale dataset of 17,000 detailed, structurally rich, and realistic residential floor plans, created to advance spatial AI research. Each plan includes precise annotations of architectural elements (walls, doors, windows, balconies) and functional spaces (such as kitchens, bedrooms, and bathrooms). ResPlan addresses key limitations of existing datasets such as RPLAN (Wu et al., 2019) and MSD (van Engelenburg et al., 2024) by offering enhanced visual fidelity and greater structural diversity, reflecting realistic and non-idealized residential layouts. Designed as a versatile, general-purpose resource, ResPlan supports a wide range of applications including robotics, reinforcement learning, generative AI, virtual and augmented reality, simulations, and game development. Plans are provided in both geometric and graph-based formats, enabling direct integration into simulation engines and fast 3D conversion. A key contribution is an open-source pipeline for geometry cleaning, alignment, and annotation refinement. Additionally, ResPlan includes structured representations of room connectivity, supporting graph-based spatial reasoning tasks. Finally, we present comparative analyses with existing benchmarks and outline several open benchmark tasks enabled by ResPlan. Ultimately, ResPlan offers a significant advance in scale, realism, and usability, providing a robust foundation for developing and benchmarking next-generation spatial intelligence systems.

In this paper, we propose to use the general L^2-based Sobolev norms, i.e., H^s norms where sin R, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As opposed to a popular trend of developing regularization methods, we emphasize that an implicit regularization effect can be achieved through the class of Sobolev norms as the data-fitting term. Specifically, we analyze that the implicit regularization comes from the weights that the H^s norm imposes on different frequency contents of an underlying image. We further analyze the underlying noise assumption of using the Sobolev norm as the data-fitting term from a Bayesian perspective, build the connections with the Sobolev gradient-based methods and discuss the preconditioning effects on the convergence rate of the gradient descent algorithm, leading to a better understanding of functional spaces/metrics and the optimization process involved in image processing. Numerical results in full waveform inversion, image denoising and deblurring demonstrate the implicit regularization effects.

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

We introduce the task of predicting functional 3D scene graphs for real-world indoor environments from posed RGB-D images. Unlike traditional 3D scene graphs that focus on spatial relationships of objects, functional 3D scene graphs capture objects, interactive elements, and their functional relationships. Due to the lack of training data, we leverage foundation models, including visual language models (VLMs) and large language models (LLMs), to encode functional knowledge. We evaluate our approach on an extended SceneFun3D dataset and a newly collected dataset, FunGraph3D, both annotated with functional 3D scene graphs. Our method significantly outperforms adapted baselines, including Open3DSG and ConceptGraph, demonstrating its effectiveness in modeling complex scene functionalities. We also demonstrate downstream applications such as 3D question answering and robotic manipulation using functional 3D scene graphs. See our project page at https://openfungraph.github.io

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Generating novel molecules with out-of-distribution properties is a major challenge in molecular discovery. While supervised learning methods generate high-quality molecules similar to those in a dataset, they struggle to generalize to out-of-distribution properties. Reinforcement learning can explore new chemical spaces but often conducts 'reward-hacking' and generates non-synthesizable molecules. In this work, we address this problem by integrating a state-of-the-art supervised learning method, STGG+, in an active learning loop. Our approach iteratively generates, evaluates, and fine-tunes STGG+ to continuously expand its knowledge. We denote this approach STGG+AL. We apply STGG+AL to the design of organic pi-functional materials, specifically two challenging tasks: 1) generating highly absorptive molecules characterized by high oscillator strength and 2) designing absorptive molecules with reasonable oscillator strength in the near-infrared (NIR) range. The generated molecules are validated and rationalized in-silico with time-dependent density functional theory. Our results demonstrate that our method is highly effective in generating novel molecules with high oscillator strength, contrary to existing methods such as reinforcement learning (RL) methods. We open-source our active-learning code along with our Conjugated-xTB dataset containing 2.9 million pi-conjugated molecules and the function for approximating the oscillator strength and absorption wavelength (based on sTDA-xTB).

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

For the evolutionary Stokes problem with dynamic boundary condition we show maximal regularity of weak solutions in time. Due to the characteriation of R-sectorial operators on Hilbert spaces, the proof reduces to finding the correct functional analytic setting and proving that an operator is sectorial, i.e. generates an analytic semigroup.

Accelerated materials discovery is an urgent demand to drive advancements in fields such as energy conversion, storage, and catalysis. Property-directed generative design has emerged as a transformative approach for rapidly discovering new functional inorganic materials with multiple desired properties within vast and complex search spaces. However, this approach faces two primary challenges: data scarcity for functional properties and the multi-objective optimization required to balance competing tasks. Here, we present a multi-property-directed generative framework designed to overcome these limitations and enhance site symmetry-compliant crystal generation beyond P1 (translational) symmetry. By incorporating Wyckoff-position-based data augmentation and transfer learning, our framework effectively handles sparse and small functional datasets, enabling the generation of new stable materials simultaneously conditioned on targeted space group, band gap, and formation energy. Using this approach, we identified previously unknown thermodynamically and lattice-dynamically stable semiconductors in tetragonal, trigonal, and cubic systems, with bandgaps ranging from 0.13 to 2.20 eV, as validated by density functional theory (DFT) calculations. Additionally, we assessed their thermoelectric descriptors using DFT, indicating their potential suitability for thermoelectric applications. We believe our integrated framework represents a significant step forward in generative design of inorganic materials.

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square summability of Dirichlet coefficients for every s > 1, with a Banach component controlling logarithmic averages of partial sums. We prove that U is a complete Banach space which embeds continuously all standard Hilbert spaces of Dirichlet series and allows natural actions of Dirichlet convolution and shift operators. This framework provides a unified analytic setting for classical and modern problems in multiplicative number theory.

We present UniTEX, a novel two-stage 3D texture generation framework to create high-quality, consistent textures for 3D assets. Existing approaches predominantly rely on UV-based inpainting to refine textures after reprojecting the generated multi-view images onto the 3D shapes, which introduces challenges related to topological ambiguity. To address this, we propose to bypass the limitations of UV mapping by operating directly in a unified 3D functional space. Specifically, we first propose that lifts texture generation into 3D space via Texture Functions (TFs)--a continuous, volumetric representation that maps any 3D point to a texture value based solely on surface proximity, independent of mesh topology. Then, we propose to predict these TFs directly from images and geometry inputs using a transformer-based Large Texturing Model (LTM). To further enhance texture quality and leverage powerful 2D priors, we develop an advanced LoRA-based strategy for efficiently adapting large-scale Diffusion Transformers (DiTs) for high-quality multi-view texture synthesis as our first stage. Extensive experiments demonstrate that UniTEX achieves superior visual quality and texture integrity compared to existing approaches, offering a generalizable and scalable solution for automated 3D texture generation. Code will available in: https://github.com/YixunLiang/UniTEX.