arXiv subjects

Davide Staub

Publications and source records attributed to Davide Staub.

3 recordsLinked to original sources

arXiv2026

Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for solving Partial Differential Equations (PDEs), offering a meshfree alternative that integrates physical principles into the learning process. This presents a new paradigm compared to traditional discretization methods and purely data-driven machine learning techniques. While promising, PINNs are not a panacea; they inherit challenges such as spectral bias and unstable convergence. Moreover, their potential in seismology remains largely unexplored. In this work, we provide a robust and critical assessment of PINNs for solving the elastic wave equation in seismology. We investigate the performance of PINNs on problems with varying degrees of complexity across various seismic sources and parameter models, from constant to highly heterogeneous settings. A pivotal aspect of our work involves investigating whether embedding physical principles directly into the network architecture enhances convergence and accuracy. We test an extensive range of neural architecture designs, from unrestricted, uninformed PINNs to highly specialized ones. We find that integrating an understanding of wave physics into the network design significantly improves accuracy. For instance, introducing a custom wavelet or plane wave layer, coupled with encoder and decoder layers, consistently yields a relative $L_2$ error approximately half that of the standard PINN, as evidenced across numerous experiments. We further demonstrate that this novel architecture enhances accuracy when applied to the acoustic wave equation, underlying the versatility of our network. Another key contribution of our research is the successful conditioning of PINNs on seismic source locations. This signifies a considerable advancement towards rapid seismic hazard detection and seismic analysis.

cs.LG↗

arXiv2026

Cross-lingual brain-language model alignment is robust but challenges hierarchical and computational accounts

Brain-language model alignment is often interpreted as evidence that transformer models implement computations similar to those of the human brain. This assumes that neural predictivity reflects internal computational properties of large language models (LLMs), such as hierarchical contextual processing, predictive coding, or representational compression. An alternative possibility is that brain scores primarily reflect stable lexical-semantic correspondences shared by language models and the brain. Here we tested these interpretations using whole-brain encoding models across Mandarin, English, and French. Across all three languages, transformer representations significantly predicted activity in a distributed network spanning classical language regions, transmodal cortical systems, and subcortical structures. These spatial patterns showed substantial cross-linguistic overlap and remained remarkably stable across layers, providing little evidence that model depth systematically maps onto cortical processing hierarchies. Likewise, contextual transformer embeddings did not consistently outperform static lexical embeddings, despite providing some unique predictive variance. Finally, neither surprisal nor intrinsic dimensionality reproduced the layer-wise profile of brain scores, arguing against prediction and information compression as primary explanations for brain-LLM alignment. Together, these findings suggest that brain-LLM alignment is more robust across languages, transformer depth, and model architectures than previously appreciated, but less informative about shared computational mechanisms. Our results are more consistent with neural predictivity reflecting stable representational structure preserved across model transformations than with a one-to-one correspondence between their underlying computations.

cs.CL↗

arXiv2025

Coherence in the brain unfolds across separable temporal regimes

To maintain coherence in language, the brain must satisfy key competing temporal demands: the gradual accumulation of meaning across extended context (drift) and the rapid reconfiguration of representations at event boundaries (shift). How these processes are implemented in the human brain during naturalistic listening remains unclear. Here, we tested whether both can be captured by annotation-free drift and shift signals and whether their neural expression shows distinct regional preferences across the brain. These signals were derived from a large language model (LLM) processing the narrative input. To enable high-precision voxelwise encoding models with stable parameter estimates, we densely sampled one healthy adult across more than 7 hours of listening to crime stories while collecting 7 Tesla fMRI data. We then modeled the feature-informed hemodynamic response using a regularized encoding framework validated on independent stories. Drift predictions were prevalent in default-mode network hubs, whereas shift predictions were evident bilaterally in the primary auditory cortex and language association cortex. Together, these findings show that coherence during language comprehension is implemented through distinct but co-expressed neural regimes of slow contextual integration and rapid event-driven reconfiguration, offering a mechanistic entry point for understanding disturbances of language coherence in psychiatric disorders.

q-bio.NC↗