In many problems in physics and engineering, one encounters complicated differential equations with strongly scale-dependent terms for which exact analytical or numerical solutions are not available. A common strategy is to divide the domain into several regions (patches) and simplify the equation in each region. When approximate analytic solutions can be obtained in each patch, they are then matched at the interfaces to construct a global solution. However, this patching procedure can fail to reproduce the correct solution, since the approximate forms may break down near the matching boundaries. In this work, we propose a learning framework in which the integration constants of asymptotic analytic solutions are promoted to scale-dependent functions. By constraining these coefficient functions with the original differential equation over the domain, the network learns a globally valid solution that smoothly interpolates between asymptotic regimes, eliminating the need for arbitrary boundary matching. We demonstrate the effectiveness of this framework in representative problems from chemical kinetics and cosmology, where it accurately reproduces global solutions and outperforms conventional matching procedures.
As ancient stellar systems, globular clusters (GCs) offer valuable insights into the dynamical histories of large galaxies. Previous studies of GC populations in the inner and outer regions of the Andromeda Galaxy (M31) have revealed intriguing subpopulations with distinct kinematic properties. Here, we build upon earlier studies by employing Bayesian modelling to investigate the kinematics of the combined inner and outer GC populations of M31. Given the heterogeneous nature of the data, we examine subpopulations defined by GCs' metallicity and by associations with substructure, in order to characterise possible relationships between the inner and outer GC populations. We find that lower-metallicity GCs and those linked to substructures exhibit a common, more rapid rotation, whose alignment is distinct from that of higher-metallicity and non-substructure GCs. Furthermore, the higher-metallicity GCs rotate in alignment with Andromeda's stellar disk. These pronounced kinematic differences reinforce the idea that different subgroups of GCs were accreted to M31 at distinct epochs, shedding light on the complex assembly history of the galaxy.
We present MARVEL (https://ligogpt.mit.edu/marvel), a locally deployable, open-source framework for domain-aware question answering and assisted scientific research. It is designed to address the increasing demands of a digital assistant for scientific groups that can read highly technical data, cite precisely, and operate within authenticated networks. MARVEL combines a fast path for straightforward queries with a more deliberate DeepSearch mode that integrates retrieval-augmented generation and Monte Carlo Tree Search. It explores complementary subqueries, allocates more compute to promising branches, and maintains a global evidence ledger that preserves sources during drafting. We applied this framework in the context of gravitational-wave research related to the Laser Interferometer Gravitational-wave Observatory. Answers are grounded in a curated semantic index of research literature, doctoral theses, LIGO documents, and long-running detector electronic logbooks, with targeted web searches when appropriate. Because direct benchmarking against commercial LLMs cannot be performed on private data, we evaluated MARVEL on two publicly available surrogate datasets that capture comparable semantic and technical characteristics. On these benchmarks, MARVEL matches a GPT-4o mini baseline on literature-centric queries and substantially outperforms it on detector-operations content, where domain retrieval and guided reasoning are decisive. By making the complete framework and evaluation datasets openly available, we aim to provide a reproducible foundation for developing domain-specific scientific assistants.