arXiv:2606. 06094v1 Announce Type: cross Abstract: Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning.
arXiv:2606. 15637v1 Announce Type: new Abstract: A digital twin (DT) of a patient-specific heart offers significant potential in personalized medicine.
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv:2607. 07425v1 Announce Type: cross Abstract: Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data.
arXiv:2608. 03927v1 Announce Type: new Abstract: Engineered Skeletal Muscle Tissues (ESMs) have become a key structure for biomedical disease modeling and pharmacological screening, yet their functional characterization often relies on simplistic metrics like peak force, discarding critical kinetic information.
arXiv:2606. 02145v1 Announce Type: new Abstract: Accurate prediction of polymerization dynamics is essential for process design, control, and optimization.
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv:2510. 09685v2 Announce Type: replace-cross Abstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines.
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.
arXiv:2510. 14656v3 Announce Type: replace-cross Abstract: This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement.
arXiv:2606. 30398v1 Announce Type: new Abstract: Accurately predicting the temporal evolution of clinical biomarkers is crucial for the early diagnosis and management of neurodegenerative diseases such as Alzheimer's disease.