Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is to accurately infer the parameters, particularly when the parameters exhibit non-linear and spatiotemporal variations. Existing parameter estimation methods, such as sparse identification, physics-informed neural networks (PINNs), and neural operators, struggle in such cases, especially with nonlinear dynamics, multiphysics interactions, or limited observations of the system response. To address this, we introduce Neptune, a versatile method capable of inferring parameter fields from sparse measurements of system responses. Neptune employs independent coordinate neural networks to continuously represent each parameter field in physical space or in state variables. Across various physical and biomedical problems, where direct parameter measurements are prohibitively expensive or unattainable, Neptune significantly outperforms existing methods, achieving robust parameter estimation from as few as 45 measurements, reducing parameter estimation errors by up to two orders of magnitude and dynamic response prediction errors by a factor of ten to baseline methods. More importantly, it exhibits superior physical extrapolation capabilities, enabling reliable predictions in regimes far beyond the training data. By facilitating data-efficient parameter inference, Neptune promises significant utility in engineering, healthcare, and beyond.
This work introduces a pioneering exploration of Self-Supervised Learning (SSL) within the SNN, and proposes a novel Spiking Self-Attention (SSA) and Spiking Transformer (Spikformer) that achieves 80+% accuracy on ImageNet.
Zhaokun Zhou, Kaiwei Che, Wei Fang et al.· arXiv.org· 69 citations· ⚡10
EquiPocket is proposed, an E(3)-equivariant Graph Neural Network for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms.
Yang Zhang, Wenbing Huang, Zhewei Wei et al.· International Conference on...· 43 citations· ⚡4
It is shown that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension, which proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014) and determines the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct conclusion. Mathematically, a measurement operator is Hermitian with eigenvalues in [0,1]. By noticing that this constraint on each eigenvalue is the same as that imposed on fermions by the Pauli exclusion principle, we interpret every eigenmode of a measurement operator as an independent effective fermionic mode. Under this perspective, various objective functions in quantum hypothesis testing can be viewed as the total expected energy associated with these fermionic occupation numbers. By instead fixing a temperature and minimizing the total expected fermionic free energy, we find that optimal measurements for these modified objective functions are Fermi-Dirac thermal measurements, wherein their eigenvalues are specified by Fermi-Dirac distributions. In the low-temperature limit, their performance closely approximates that of optimal measurements for quantum hypothesis testing, and we show that their parameters can be learned by classical or hybrid quantum-classical optimization algorithms. This leads to a new quantum machine-learning model, termed Fermi-Dirac machines, consisting of parameterized Fermi-Dirac thermal measurements-an alternative to quantum Boltzmann machines based on thermal states. Beyond hypothesis testing, we show how general semidefinite optimization problems can be solved using this approach, leading to a novel paradigm for semidefinite optimization on quantum computers, in which the goal is to implement thermal measurements rather than prepare thermal states. Finally, we propose quantum algorithms for implementing Fermi-Dirac thermal measurements, and we also propose second-order hybrid quantum-classical optimization algorithms.
This systematic review evaluates 55 studies from 2017 to 2023 on the application of machine learning techniques to ASD, highlighting key challenges and opportunities, particularly the need for models that can integrate complex data to improve diagnostic accuracy and treatment outcomes.
Rafael Muñoz-Terol, Jesús Peral, Sandra Amador et al.· Heliyon· 4 citations· ⚡1
SimulRAG, a simulator-based RAG framework with a generalized retrieval interface that translates between text and simulator parameters/outputs, is proposed, which improves informativeness and factuality over the strongest adapted RAG baselines, while UE+SBA enhances claim-level efficiency and quality.
Haozhou Xu, D. Wu, M. Chinazzi et al.· arXiv.org· 3 citations
Related blog posts
MIT News · Artificial Intelligence· news.mit.eduAug 18, 2026
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
