Effective surrogate models are critical for accelerating scientific simulations. Implicit neural representations (INRs) offer a compact and continuous framework for modeling spatially structured data, but they often struggle with complex scientific fields exhibiting localized, high-frequency variations. Recent approaches address this by introducing additional features along rigid geometric structures (e.g., grids), but at the cost of flexibility and increased model size. In this paper, we propose a simple yet effective alternative: Feature-Adaptive INR (FA-INR). FA-INR leverages cross-attention to an augmented memory bank to learn flexible feature representations, enabling adaptive allocation of model capacity based on data characteristics, rather than rigid structural assumptions. To further improve scalability, we introduce a coordinate-guided mixture of experts (MoE) that enhances the specialization and efficiency of feature representations. Experiments on three large-scale ensemble simulation datasets show that FA-INR achieves state-of-the-art fidelity while significantly reducing model size, establishing a new trade-off frontier between accuracy and compactness for INR-based surrogates.

Scientific problem-solving involves synthesizing information while applying expert knowledge. We introduce CURIE, a scientific long-Context Understanding,Reasoning and Information Extraction benchmark to measure the potential of Large Language Models (LLMs) in scientific problem-solving and assisting scientists in realistic workflows. This benchmark introduces ten challenging tasks with a total of 580 problems and solution pairs curated by experts in six disciplines - materials science, condensed matter physics, quantum computing, geospatial analysis, biodiversity, and proteins - covering both experimental and theoretical work-flows in science. We evaluate a range of closed and open LLMs on tasks in CURIE which requires domain expertise, comprehension of long in-context information,and multi-step reasoning. While Gemini Flash 2.0 and Claude-3 show consistent high comprehension across domains, the popular GPT-4o and command-R+ fail dramatically on protein sequencing tasks. With the best performance at 32% there is much room for improvement for all models. We hope that insights gained from CURIE can guide the future development of LLMs in sciences. Evaluation code and data are in https://github.com/google/curie

Deep neural networks (DNNs) and probabilistic graphical models (PGMs) are the two main tools for statistical modeling. While DNNs provide the ability to model rich and complex relationships between input and output variables, PGMs provide the ability to encode dependencies among the output variables themselves. End-to-end training methods for models with structured graphical dependencies on top of neural predictions have recently emerged as a principled way of combining these two paradigms. While these models have proven to be powerful in discriminative settings with discrete outputs, extensions to structured continuous spaces, as well as performing efficient inference in these spaces, are lacking. We propose non-parametric structured output networks (NSON), a modular approach that cleanly separates a non-parametric, structured posterior representation from a discriminative inference scheme but allows joint end-to-end training of both components. Our experiments evaluate the ability of NSONs to capture structured posterior densities (modeling) and to compute complex statistics of those densities (inference). We compare our model to output spaces of varying expressiveness and popular variational and sampling-based inference algorithms.

Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity. Furthermore, all prevalent architectures for PDE solving lack at least one of several desirable properties of an ideal surrogate model, such as (i) generalization to PDE parameters not seen during training, (ii) spatial and temporal zero-shot super-resolution, (iii) continuous temporal extrapolation, (iv) support for 1D, 2D, and 3D PDEs, and (v) efficient inference for longer temporal rollouts. To address these limitations, we propose Vectorized Conditional Neural Fields (VCNeFs), which represent the solution of time-dependent PDEs as neural fields. Contrary to prior methods, however, VCNeFs compute, for a set of multiple spatio-temporal query points, their solutions in parallel and model their dependencies through attention mechanisms. Moreover, VCNeF can condition the neural field on both the initial conditions and the parameters of the PDEs. An extensive set of experiments demonstrates that VCNeFs are competitive with and often outperform existing ML-based surrogate models.

Deep reinforcement learning algorithms typically act on the same set of actions. However, this is not sufficient for a wide range of real-world applications where different subsets are available at each step. In this thesis, we consider the problem of interval restrictions as they occur in pathfinding with dynamic obstacles. When actions that lead to collisions are avoided, the continuous action space is split into variable parts. Recent research learns with strong assumptions on the number of intervals, is limited to convex subsets, and the available actions are learned from the observations. Therefore, we propose two approaches that are independent of the state of the environment by extending parameterized reinforcement learning and ConstraintNet to handle an arbitrary number of intervals. We demonstrate their performance in an obstacle avoidance task and compare the methods to penalties, projection, replacement, as well as discrete and continuous masking from the literature. The results suggest that discrete masking of action-values is the only effective method when constraints did not emerge during training. When restrictions are learned, the decision between projection, masking, and our ConstraintNet modification seems to depend on the task at hand. We compare the results with varying complexity and give directions for future work.

Deep neural networks (DNNs) and probabilistic graphical models (PGMs) are the two main tools for statistical modeling. While DNNs provide the ability to model rich and complex relationships between input and output variables, PGMs provide the ability to encode dependencies among the output variables themselves. End-to-end training methods for models with structured graphical dependencies on top of neural predictions have recently emerged as a principled way of combining these two paradigms. While these models have proven to be powerful in discriminative settings with discrete outputs, extensions to structured continuous spaces, as well as performing efficient inference in these spaces, are lacking. We propose non-parametric structured output networks (NSON), a modular approach that cleanly separates a non-parametric, structured posterior representation from a discriminative inference scheme but allows joint end-to-end training of both components. Our experiments evaluate the ability of NSONs to capture structured posterior densities (modeling) and to compute complex statistics of those densities (inference). We compare our model to output spaces of varying expressiveness and popular variational and sampling-based inference algorithms.