Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies.

In the realm of interpretability and out-of-distribution generalisation, the identifiability of latent variable models has emerged as a captivating field of inquiry. In this work, we delve into the identifiability of Switching Dynamical Systems, taking an initial stride toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds ($1\textrm{fs}=10^{-15}\textrm{s}$). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of $10^{5} - 10^{6}\:\textrm{fs}$. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about $7\times 10^6$ parameters.

Forecasting natural gas consumption, considering seasonality and trends, is crucial in planning its supply and consumption and optimizing the cost of obtaining it, mainly by industrial entities. However, in times of threats to its supply, it is also a critical element that guarantees the supply of this raw material to meet individual consumers' needs, ensuring society's energy security. This article introduces a novel multistep ahead forecasting of natural gas consumption with change point detection integration for model collection selection with continual learning capabilities using data stream processing. The performance of the forecasting models based on the proposed approach is evaluated in a complex real-world use case of natural gas consumption forecasting. We employed Hoeffding tree predictors as forecasting models and the Pruned Exact Linear Time (PELT) algorithm for the change point detection procedure. The change point detection integration enables selecting a different model collection for successive time frames. Thus, three model collection selection procedures (with and without an error feedback loop) are defined and evaluated for forecasting scenarios with various densities of detected change points. These models were compared with change point agnostic baseline approaches. Our experiments show that fewer change points result in a lower forecasting error regardless of the model collection selection procedure employed. Also, simpler model collection selection procedures omitting forecasting error feedback leads to more robust forecasting models suitable for continual learning tasks.

Ray tracing (RT) is instrumental in 6G research in order to generate spatially-consistent and environment-specific channel impulse responses (CIRs). While acquiring accurate scene geometries is now relatively straightforward, determining material characteristics requires precise calibration using channel measurements. We therefore introduce a novel gradient-based calibration method, complemented by differentiable parametrizations of material properties, scattering and antenna patterns. Our method seamlessly integrates with differentiable ray tracers that enable the computation of derivatives of CIRs with respect to these parameters. Essentially, we approach field computation as a large computational graph wherein parameters are trainable akin to weights of a neural network (NN). We have validated our method using both synthetic data and real-world indoor channel measurements, employing a distributed multiple-input multiple-output (MIMO) channel sounder.

Power demand forecasting is a crucial and challenging task for new power system and integrated energy system. However, as public feature databases and the theoretical mechanism of power demand changes are unavailable, the known features of power demand fluctuation are much limited. Recently, multimodal learning approaches have shown great vitality in machine learning and AIGC. In this paper, we interact two modal data and propose a textual-knowledge-guided numerical feature discovery (TKNFD) method for short-term power demand forecasting. TKNFD extensively accumulates qualitative textual knowledge, expands it into a candidate feature-type set, collects numerical data of these features, and eventually builds four-dimensional multivariate source-tracking databases (4DM-STDs). Next, TKNFD presents a two-level quantitative feature identification strategy independent of forecasting models, finds 43-48 features, and systematically analyses feature contribution and dependency correlation. Benchmark experiments in two different regions around the world demonstrate that the forecasting accuracy of TKNFD-discovered features reliably outperforms that of SoTA feature schemes by 16.84% to 36.36% MAPE. In particular, TKNFD reveals many unknown features, especially several dominant features in the unknown energy and astronomical dimensions, which extend the knowledge on the origin of strong randomness and non-linearity in power demand fluctuation. Besides, 4DM-STDs can serve as public baseline databases.

Our work presents a novel approach to shape optimization, with the twofold objective to improve the efficiency of global optimization algorithms while promoting the generation of high-quality designs during the optimization process free of geometrical anomalies. This is accomplished by reducing the number of the original design variables defining a new reduced subspace where the geometrical variance is maximized and modeling the underlying generative process of the data via probabilistic linear latent variable models such as factor analysis and probabilistic principal component analysis. We show that the data follows approximately a Gaussian distribution when the shape modification method is linear and the design variables are sampled uniformly at random, due to the direct application of the central limit theorem. The degree of anomalousness is measured in terms of Mahalanobis distance, and the paper demonstrates that abnormal designs tend to exhibit a high value of this metric. This enables the definition of a new optimization model where anomalous geometries are penalized and consequently avoided during the optimization loop. The procedure is demonstrated for hull shape optimization of the DTMB 5415 model, extensively used as an international benchmark for shape optimization problems. The global optimization routine is carried out using Bayesian optimization and the DIRECT algorithm. From the numerical results, the new framework improves the convergence of global optimization algorithms, while only designs with high-quality geometrical features are generated through the optimization routine thereby avoiding the wastage of precious computationally expensive simulations.

Modeling the interactions between drugs, targets, and diseases is paramount in drug discovery and has significant implications for precision medicine and personalized treatments. Current approaches frequently consider drug-target or drug-disease interactions individually, ignoring the interdependencies among all three entities. Within human metabolic systems, drugs interact with protein targets in cells, influencing target activities and subsequently impacting biological pathways to promote healthy functions and treat diseases. Moving beyond binary relationships and exploring tighter triple relationships is essential to understanding drugs' mechanism of action (MoAs). Moreover, identifying the heterogeneity of drugs, targets, and diseases, along with their distinct characteristics, is critical to model these complex interactions appropriately. To address these challenges, we effectively model the interconnectedness of all entities in a heterogeneous graph and develop a novel Heterogeneous Graph Triplet Attention Network (\texttt{HeTriNet}). \texttt{HeTriNet} introduces a novel triplet attention mechanism within this heterogeneous graph structure. Beyond pairwise attention as the importance of an entity for the other one, we define triplet attention to model the importance of pairs for entities in the drug-target-disease triplet prediction problem. Experimental results on real-world datasets show that \texttt{HeTriNet} outperforms several baselines, demonstrating its remarkable proficiency in uncovering novel drug-target-disease relationships.