We present a benchmark for egocentric multimodal goal inference for assistive wearable agents. This benchmark evaluates the ability of AI systems to infer user goals from egocentric video, audio, and other sensor modalities in real-world scenarios. The dataset includes diverse real-world tasks and contexts, enabling evaluation of assistive agents that can proactively understand and support user intentions. This work is critical for developing next-generation wearable computers that can provide contextually-aware assistance.

We propose the common task framework as a mechanism for accelerating scientific discovery through collaborative machine learning. This framework establishes shared datasets, evaluation metrics, and benchmarks that enable the AI and scientific computing communities to jointly advance the state of the art in scientific machine learning. By creating common tasks analogous to those that have driven progress in computer vision and natural language processing, we aim to catalyze breakthroughs in applying AI to fundamental scientific problems.

We present DigiData, a comprehensive framework for training and evaluating general-purpose mobile control agents. This work addresses the challenge of creating AI agents that can navigate and interact with mobile user interfaces to perform tasks automatically. DigiData provides large-scale datasets, training methodologies, and benchmarks for developing digital agents that can understand mobile UI environments and execute actions on behalf of users. This research is critical for advancing the capabilities of AI assistants in mobile computing environments.

We propose LiCROM, a method that combines linear-subspace model reduction with continuous neural field representations. By representing the reduced basis using neural fields, we enable continuous queries in space and time, facilitating super-resolution reconstruction and smooth interpolation. This approach bridges classical model reduction techniques with modern neural representations, offering advantages for computer graphics applications including real-time physics simulation and animation.

We propose neural stress fields, a method for reduced-order modeling of elastoplastic materials and fracture mechanics. By representing stress fields using neural networks, we enable efficient simulation of complex material behaviors including plasticity and fracture. This approach facilitates real-time simulation of challenging scenarios in computer graphics and virtual reality applications while maintaining physical accuracy.

We propose CROM (Continuous Reduced-Order Modeling), a framework for model reduction of PDEs using implicit neural representations. By leveraging coordinate-based neural networks, CROM represents the solution manifold continuously in both space and time, enabling super-resolution queries and analytical computation of spatiotemporal derivatives. This approach combines the approximation power of neural networks with the mathematical rigor of projection-based model reduction, offering significant advantages for scientific computing and real-time simulation applications.

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. To represent the low-dimensional nonlinear manifold, we consider an implicit neural representation (INR) that parameterizes the material-point deformation map as a function of time. This enables the use of deep convolutional autoencoders for defining the nonlinear manifold, which has proven effective for model reduction in other settings. The proposed approach enables large-scale simulations to execute efficiently via model reduction, which is particularly important for virtual reality (VR) applications that require real-time performance. We demonstrate the method's ability to significantly outperform linear-subspace methods on benchmark solid-mechanics problems, including scenarios with large deformations and complex contact.

This work proposes a domain-decomposition approach for the least-squares Petrov–Galerkin (LSPG) reduced-order model. The DD-LSPG method enables reduced-order models to be constructed independently on subdomains of the computational domain, which facilitates parallel computation and enables localized basis adaptation. The method employs a nonoverlapping domain decomposition with interface conditions that ensure global consistency. Numerical experiments demonstrate that the DD-LSPG method can achieve accuracy comparable to global LSPG while enabling computational parallelism and flexibility in basis construction.

This work proposes a constrained-optimization projection framework for preserving general physical properties in model reduction of dynamical systems. The method formulates the reduced-order model as a constrained optimization problem in which the objective function penalizes deviation from the standard Galerkin or Petrov–Galerkin projection, while constraints explicitly enforce preservation of desired physical properties (e.g., conservation laws, positivity, boundedness). This framework provides a systematic approach for structure-preserving model reduction that is applicable to a wide range of physical properties and dynamical systems.

This work proposes a conservative manifold least-squares Petrov–Galerkin (LSPG) projection approach for model reduction of steady hypersonic aerodynamics. Hypersonic flows exhibit complex physics including shock waves, boundary layers, and high-temperature thermochemical effects, making them computationally expensive to simulate. The proposed method combines the conservative formulation for finite-volume discretizations with manifold LSPG projection to enable accurate and efficient reduced-order models for hypersonic aerodynamics. Numerical experiments demonstrate significant computational speedups while maintaining accuracy for engineering-relevant quantities of interest.

This work proposes a windowed least-squares approach for model reduction of dynamical systems. The method constructs reduced-order models by minimizing the residual over a sliding time window, which enables the method to adapt to the local dynamics and improve accuracy compared to traditional least-squares approaches that consider the entire time domain globally. The windowed formulation provides a natural framework for handling time-dependent phenomena and enables parallelization across time windows. Numerical experiments demonstrate the method's effectiveness for both linear and nonlinear dynamical systems.

This work proposes an approach for latent dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, we compute a low-dimensional embedding of the high-dimensional dynamical-system state using deep convolutional autoencoders. This defines a low-dimensional nonlinear manifold on which the state is subsequently enforced to evolve. Second, we define a latent dynamics model that associates with a constrained optimization problem. Specifically, the objective function is defined as the sum of squares of conservation-law violations over control volumes in a finite-volume discretization of the problem; nonlinear equality constraints explicitly enforce conservation over prescribed subdomains of the problem. The resulting dynamics model-which can be considered as a projection-based reduced-order model-ensures that the time-evolution of the latent state exactly satisfies conservation laws over the prescribed subdomains. In contrast to existing methods for latent dynamics learning, this is the only method that both employs a nonlinear embedding and computes dynamics for the latent state that guarantee the satisfaction of prescribed physical properties. Numerical experiments on a benchmark advection problem illustrate the method's ability to significantly reduce the dimensionality while enforcing physical conservation.

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution. As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis. To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves. The mechanism is based on the previously proposed adaptive $h$-refinement method for ROMs [12], but improves upon this work in two crucial ways. First, the proposed method enables basis refinement with respect to any orthogonal basis (not just the Kronecker basis), thereby generalizing the refinement mechanism and enabling it to be tailored to the physics characterizing the problem at hand. Second, the proposed method provides a fast online algorithm for periodically compressing the enriched basis via an efficient proper orthogonal decomposition (POD) method, which does not incur any operations that scale with the FOM dimension. These two features allow the proposed method to serve as (1) a failsafe mechanism for ROMs, as the method enables the ROM to satisfy any prescribed error tolerance online (even in the case of inadequate training), and (2) an efficient online basis-adaptation mechanism, as the combination of basis enrichment and compression enables the basis to adapt online while controlling its dimension.

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in [Freno, Carlberg, 2019] to dynamical systems. The proposed Time-Series Machine-Learning Error Modeling (T-MLEM) method constructs a regression model that maps features—which comprise error indicators that are derived from standard a posteriori error-quantification techniques—to a random variable for the approximate-solution error at each time instance. The proposed framework considers a wide range of candidate features, regression methods, and additive noise models. We consider primarily recursive regression techniques developed for time-series modeling, including both classical time-series models (e.g., autoregressive models) and recurrent neural networks (RNNs), but also analyze standard non-recursive regression techniques (e.g., feed-forward neural networks) for comparative purposes. Numerical experiments conducted on multiple benchmark problems illustrate that the long short-term memory (LSTM) neural network, which is a type of RNN, outperforms other methods and yields substantial improvements in error predictions over traditional approaches.

We introduce Pressio, a library for enabling projection-based model reduction for large-scale nonlinear dynamical systems. Pressio provides a non-intrusive wrapper that enables state-of-the-art nonlinear model reduction methods to be seamlessly integrated with existing high-performance computing (HPC) codes. The library is designed to be flexible, extensible, and performant, supporting a wide range of model reduction techniques including Galerkin and Petrov–Galerkin projection methods. Pressio facilitates the adoption of model reduction in production computational physics codes across many application domains.

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) POD. Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov $n$-width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov $n$-width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to extit{manifold Galerkin} projection, while the latter leads to extit{manifold least-squares Petrov–Galerkin} (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models. We also propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Finally, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic $n$-width limitations of linear subspaces.

This work introduces the network uncertainty quantification (NetUQ) method for performing uncertainty propagation in systems composed of interconnected components. The method assumes the existence of a collection of components, each of which is characterized by exogenous-input random variables (e.g., material properties), endogenous-input random variables (e.g., boundary conditions defined by another component), output random variables (e.g., quantities of interest), and a local uncertainty-propagation operator (e.g., provided by stochastic collocation) that computes output random variables from input random variables. The method assembles the full-system network by connecting components, which is achieved simply by associating endogenous-input random variables for each component with output random variables from other components; no other inter-component compatibility conditions are required. The network uncertainty-propagation problem is: Compute output random variables for all components given all exogenous-input random variables. To solve this problem, the method applies classical relaxation methods (i.e., Jacobi and Gauss–Seidel iteration with Anderson acceleration), which require only blackbox evaluations of component uncertainty-propagation operators. Compared with other available methods, this approach is applicable to any network topology (e.g., no restriction to feed-forward or two-component networks), promotes component independence by enabling components to employ tailored uncertaintypropagation operators, supports general functional representations of random variables, and requires no offline preprocessing stage. Also, because the method propagates functional representations of random variables throughout the network (and not, e.g., probability density functions), the joint distribution of any set of random variables throughout the network can be estimated a posteriori in a straightforward manner. We perform supporting convergence and error analysis and execute numerical experiments that demonstrate the weak- and strong-scaling performance of the method.