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Channel estimation is crucial in wireless communication systems. Many existing works train and test their models using the same or similar channel. However, practical channels are infinitely diverse and time-variant while data-driven algorithms often degrade on new and previously unseen channels. This prohibits the practical implementation of neural networks for channel estimation, particularly in high speed scenarios characterized by rapidly channel profile changes and very high Doppler shifts. Online training can fine-tune models to adapt to new channels, but requires high computation resource and incurs significant latency for physical-layer devices. Moreover, online training cannot exhaustively cover all possible channels because there are infinitely many possible channels. Therefore, we investigate the ability of neural networks to generalize to wireless channels. This paper proposes design criteria to generate synthetic training data, which guaranty that the resulting networks perform robustly across wireless channels, especially for very high Doppler shifts and different Doppler spectra. It ensures that offline-trained neural networks require no prior information or online training to precisely estimate the new channels. To demonstrate general applicability, we use neural networks with different levels of complexity to show that the generalization achieved appears to be independent of architecture. From simulation results, neural networks achieve a certain performance across wireless channels with different unseen power delay profiles (PDP) and Doppler shifts.

Health Indices (HIs) summarize degradation from operational data and support diagnostic and prognostic tasks in Prognostics and Health Management (PHM). Their usefulness depends on capturing degradation and interpreting system condition. Autoencoders learn such representations from unlabelled monitoring data; however, when training is driven only by reconstruction, the physical meaning of latent variables remains undefined, limiting their interpretation and diagnostic value. This work proposes a physics-constrained autoencoder that embeds system knowledge as an inductive bias in the decoder architecture and as a learning bias in the loss function. The decoder contains differentiable physical equations that receive latent variables and operating conditions as inputs, structurally guiding each latent variable to represent a predefined physical quantity and enabling component-level analysis before aggregation into a system-level HI.The methodology is benchmarked on the N-CMAPSS dataset against alternative representations. Reconstruction reaches an $R^2$ of 0.9993 and an MAE of 0.0036, comparable to fully data-driven models. After operating-condition correction, the inferred physical quantities track degradation, and their aggregation produces an HI with a Spearman correlation of 0.9791 with the ground truth, an RMSE of 0.0286, and an MAE of 0.0233. The methodology is further evaluated using a single model trained across four datasets representing distinct degradation scenarios. This model preserves component-level signatures that distinguish compression-side from expansion-side degradation without diagnostic labels.Finally, the proposed framework enables degradation trends to be visualized on component maps, providing a health representation in a form familiar to engine operators and domain experts.

Fault diagnosis in complex systems requires linking observed changes in physical quantities to the failure mechanisms that produce them. Experienced engineers perform this task by combining sensor information with knowledge of system behavior and fault propagation. Large Language Models (LLMs) can support this process, but their diagnostic reasoning depends on the availability of asset-specific engineering knowledge and on how this knowledge is represented and used during inference. This work introduces Chain of Physics (CoP), an LLM-based fault-diagnosis framework built around a Constrained Knowledge Graph (CKG) generated automatically from asset-specific reference documentation. CoP addresses failure-sensor association from textual engineering knowledge. The CKG stores diagnostic chains connecting failure modes, changes in physical quantities, and monitoring sensors. During inference, semantically similar graph paths are retrieved for each question and used as both information and in-context examples for the reasoning process. Candidate failure modes are extracted from the question and analysed independently through dedicated LLM calls, which generate plausible failure-to-observation chains. A final decision module compares these chains with the available answer choices. CoP is evaluated on the FailureSensorIQ benchmark across four industrial asset classes and three LLMs. Compared with direct prompting and conventional Retrieval-Augmented Generation (RAG), CoP improves diagnostic accuracy across all evaluated models, with gains ranging from 7.8 to 19.6 percentage points and from 11.7 to 18.2 percentage points, respectively. The results show that structured engineering knowledge can improve LLM-based diagnostic reasoning when graph retrieval is combined with in-context examples of fault propagation.

Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, and how their accuracy depends on their size is known only empirically. We introduce FUTON (Fourier Tensor Network), which models signals as generalized Fourier series whose coefficients are parameterized by a low-rank tensor decomposition, read out by a linear or MLP head. FUTON combines complementary inductive biases: Fourier bases capture smoothness and periodicity, while the low-rank parameterization enforces low-dimensional spectral structure. Beyond universal approximation, we show that with a linear head, the best FUTON's error splits exactly into the truncation of the signal's series and the best low-rank error of its coefficients, which we bracket from the samples before training, with a FUTON that attains the upper bound. On image fitting, occupancy volumes, and novel view synthesis, against twelve INRs of matched size, FUTON achieves the best average quality, reaches the final quality of each task's strongest baseline 4-34x sooner than that baseline, infers fastest, and trains in the least memory.