This study proposes a hybrid deep learning model for forecasting the price of Bitcoin, as the digital currency is known to exhibit frequent fluctuations. The models used are the Variational Mode Decomposition (VMD) and the Long Short-Term Memory (LSTM) network. First, VMD is used to decompose the original Bitcoin price series into Intrinsic Mode Functions (IMFs). Each IMF is then modeled using an LSTM network to capture temporal patterns more effectively. The individual forecasts from the IMFs are aggregated to produce the final prediction of the original Bitcoin Price Series. To determine the prediction power of the proposed hybrid model, a comparative analysis was conducted against the standard LSTM. The results confirmed that the hybrid VMD+LSTM model outperforms the standard LSTM across all the evaluation metrics, including RMSE, MAE and R2 and also provides a reliable 30-day forecast.

Integrated wind-solar-wave marine energy systems hold broad promise for supplying clean electricity in offshore and coastal regions. By leveraging the spatiotemporal complementarity of multiple resources, such systems can effectively mitigate the intermittency and volatility of single-source outputs, thereby substantially improving overall power-generation efficiency and resource utilization. Accurate ultra-short-term forecasting is crucial for ensuring secure operation and optimizing proactive dispatch. However, most existing forecasting methods construct separate models for each energy source, insufficiently account for the complex couplings among multiple energies, struggle to capture the system's nonlinear and nonstationary dynamics, and typically depend on extensive manual parameter tuning-limitations that constrain both predictive performance and practicality. We address this issue using a Bayesian-optimized Multivariate Variational Mode Decomposition-Long Short-Term Memory (MVMD-LSTM) framework. The framework first applies MVMD to jointly decompose wind, solar and wave power series so as to preserve cross-source couplings; it uses Bayesian optimization to automatically search the number of modes and the penalty parameter in the MVMD process to obtain intrinsic mode functions (IMFs); finally, an LSTM models the resulting IMFs to achieve ultra-short-term power forecasting for the integrated system. Experiments based on field measurements from an offshore integrated energy platform in China show that the proposed framework significantly outperforms benchmark models in terms of MAPE, RMSE and MAE. The results demonstrate superior predictive accuracy, robustness, and degree of automation.

This paper proposes a novel multimodal deep learning framework integrating bidirectional LSTM, multi-head attention mechanism, and variational mode decomposition (BiLSTM-AM-VMD) for early liver cancer diagnosis. Using heterogeneous data that include clinical characteristics, biochemical markers, and imaging-derived variables, our approach improves both prediction accuracy and interpretability. Experimental results on real-world datasets demonstrate superior performance over traditional machine learning and baseline deep learning models.

Financial time series forecasting relies on historical data and time series modeling to predict key financial indicators, such as stock prices, indexes, returns, and volatility. Accurate forecasting helps identify market trends and volatility, supports national financial regulation, and assists institutional investors in making informed investment decisions. Traditional econometric models include ARCH (Autoregressive Conditional Heteroske-dasticity Model) and GARCH (Generalized-ARCH), which describe volatility clustering and leptokurtosis in financial time series [1][2]. In the 21st century, deep learning has become prominent. Neural network models such as convolutional neural networks (CNN), deep belief networks (DBN), and autoencoders (AE) have been widely applied to sequence prediction. Among these, recurrent neural networks (RNNs) and particularly long short-term memory (LSTM) networks [3], introduced by Hochreiter and Schmidhuber in 1997 [4], address vanishing gradient problems and are suitable for capturing long-term dependencies.

Bitcoin is one of the cryptocurrencies that is gaining more popularity in recent years. Previous studies have shown that closing price alone is not enough to forecast stock market series. We introduce a new set of time series and demonstrate that a subset is necessary to improve directional accuracy based on a machine learning ensemble. In our experiments, we study which time series and machine learning algorithms deliver the best results. We found that the most relevant time series that contribute to improving directional accuracy are Open, High and Low, with the largest contribution of Low in combination with an ensemble of Gated Recurrent Unit network and a baseline forecast. The relevance of other Bitcoin-related features that are not price-related is negligible. The proposed method delivers similar performance to the state-of-the-art when observing directional accuracy.

Time-series forecasting often faces challenges due to data volatility, which can lead to inaccurate predictions. Variational Mode Decomposition (VMD) has emerged as a promising technique to mitigate volatility by decomposing data into distinct modes, thereby enhancing forecast accuracy. In this study, we integrate VMD with linear models to develop a robust forecasting framework. Our approach is evaluated on 13 diverse datasets, including ETTm2, WindTurbine, M4, and 10 air quality datasets from various Southeast Asian cities. The effectiveness of the VMD strategy is assessed by comparing Root Mean Squared Error (RMSE) values from models utilizing VMD against those without it. Additionally, we benchmark linear-based models against well-known neural network architectures such as LSTM, Bidirectional LSTM, and RNN. The results demonstrate a significant reduction in RMSE across nearly all models following VMD application. Notably, the Linear + VMD model achieved the lowest average RMSE in univariate forecasting at 0.619. In multivariate forecasting, the DLinear + VMD model consistently outperformed others, attaining the lowest RMSE across all datasets with an average of 0.019. These findings underscore the effectiveness of combining VMD with linear models for superior time-series forecasting.

The significant fluctuations in stock index prices in recent years highlight the critical need for accurate forecasting to guide investment and financial strategies. This study introduces a novel composite forecasting framework that integrates variational mode decomposition (VMD), PatchTST, and adaptive scale-weighted layer (ASWL) to address these challenges. Utilizing datasets of four major stock indices--SP500, DJI, SSEC, and FTSE--from 2000 to 2024, the proposed method first decomposes the raw price series into intrinsic mode functions (IMFs) using VMD. Each IMF is then modeled with PatchTST to capture temporal patterns effectively. The ASWL module is applied to incorporate scale information, enhancing prediction accuracy. The final forecast is derived by aggregating predictions from all IMFs. The VMD-PatchTST-ASWL framework demonstrates significant improvements in forecasting accuracy compared to traditional models, showing robust performance across different indices. This innovative approach provides a powerful tool for stock index price forecasting, with potential applications in various financial analysis and investment decision-making contexts.

For example, combining ARIMA with various decomposition algorithms such as Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) for predicting complex time series; For example, using an improved ARMA model for stock market forecasting. However, the above models need to be built on the basis of stable sequence data, and usually require testing and preprocessing of the original data, which may lead to the loss of some hidden information, especially in big data samples, and this disadvantage is easily magnified. With the development of computer technology, intelligent models represented by artificial neural networks (ANNs) are gradually emerging. This type of model is good at handling incomplete, fuzzy, uncertain, or irregular data, and has a good fit to nonlinear relationships. Shallow neural networks represented by backpropagation neural networks (BPNN) and shallow machine learning represented by support vector machines (SVM) are also widely used in financial market prediction. However, shallow neural networks do not consider the temporal nature of data, and financial time series often have certain long-term dependencies. Therefore, recurrent neural networks (RNNs) with memory function have become the latest choice. The output of RNN at a certain moment can be used as input to feedback to neurons again, and this cascade structure is very suitable for time series data, which can preserve the dependency relationships in the data.

Emotion recognition (ER) from speech signals is a robust approach since it cannot be imitated like facial expression or text based sentiment analysis. Valuable information underlying the emotions are significant for human-computer interactions enabling intelligent machines to interact with sensitivity in the real world. Previous ER studies through speech signal processing have focused exclusively on associations between different signal mode decomposition methods and hidden informative features. However, improper decomposition parameter selections lead to informative signal component losses due to mode duplicating and mixing. In contrast, the current study proposes VGG-optiVMD, an empowered variational mode decomposition algorithm, to distinguish meaningful speech features and automatically select the number of decomposed modes and optimum balancing parameter for the data fidelity constraint by assessing their effects on the VGG16 flattening output layer. Various feature vectors were employed to train the VGG16 network on different databases and assess VGG-optiVMD reproducibility and reliability. One, two, and three-dimensional feature vectors were constructed by concatenating Mel-frequency cepstral coefficients, Chromagram, Mel spectrograms, Tonnetz diagrams, and spectral centroids. Results confirmed a synergistic relationship between the fine-tuning of the signal sample rate and decomposition parameters with classification accuracy, achieving state-of-the-art 96.09% accuracy in predicting seven emotions on the Berlin EMO-DB database.

Time series forecasting represents a significant and challenging task across various fields. Recently, methods based on mode decomposition have dominated the forecasting of complex time series because of the advantages of capturing local characteristics and extracting intrinsic modes from data. Unfortunately, most models fail to capture the implied volatilities that contain significant information. To enhance the prediction of contemporary diverse and complex time series, we propose a novel time series forecasting paradigm that integrates decomposition with the capability to capture the underlying fluctuation information of the series. In our methodology, we implement the Variational Mode Decomposition algorithm to decompose the time series into K distinct sub-modes. Following this decomposition, we apply the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to extract the volatility information in these sub-modes. Subsequently, both the numerical data and the volatility information for each sub-mode are harnessed to train a neural network. This network is adept at predicting the information of the sub-modes, and we aggregate the predictions of all sub-modes to generate the final output. By integrating econometric and artificial intelligence methods, and taking into account both the numerical and volatility information of the time series, our proposed framework demonstrates superior performance in time series forecasting, as evidenced by the significant decrease in MSE, RMSE, and MAPE in our comparative experimental results.