The dynamic nature of proteins is crucial for determining their biological functions and properties, and molecular dynamics (MD) simulations stand as a predominant tool to study such phenomena. By utilizing empirically derived force fields, MD simulations explore the conformational space through numerically evolving the system along MD trajectories. However, the high-energy barrier of the force fields can hamper the exploration of MD, resulting in inadequately sampled ensemble. In this paper, we propose leveraging score-based generative models (SGMs) trained on general protein structures to perform protein conformational sampling to complement traditional MD simulations. We argue that SGMs can provide a novel framework as an alternative to traditional enhanced sampling methods by learning multi-level score functions, which directly sample a diversity-controllable ensemble of conformations. We demonstrate the effectiveness of our approach on several benchmark systems by comparing the results with long MD trajectories and state-of-the-art generative structure prediction models. Our framework provides new insights that SGMs have the potential to serve as an efficient and simulation-free methods to study protein dynamics.

We introduce a deep learning accelerated methodology to solve PDE-based Bayesian inverse problems with guaranteed accuracy. This is motivated by the ill-posed problem of inferring a spatio-temporal heat-flux parameter known as the Biot number given temperature data, however the methodology is generalisable to other settings. To accelerate Bayesian inference, we develop a novel training scheme that uses data to adaptively train a neural-network surrogate simulating the parametric forward model. By simultaneously identifying an approximate posterior distribution over the Biot number, and weighting a physics-informed training loss according to this, our approach approximates forward and inverse solution together without any need for external solves. Using a random Chebyshev series, we outline how to approximate a Gaussian process prior, and using the surrogate we apply Hamiltonian Monte Carlo (HMC) to sample from the posterior distribution. We derive convergence of the surrogate posterior to the true posterior distribution in the Hellinger metric as our adaptive loss approaches zero. Additionally, we describe how this surrogate-accelerated HMC approach can be combined with traditional PDE solvers in a delayed-acceptance scheme to a-priori control the posterior accuracy. This overcomes a major limitation of deep learning-based surrogate approaches, which do not achieve guaranteed accuracy a-priori due to their non-convex training. Biot number calculations are involved in turbo-machinery design, which is safety critical and highly regulated, therefore it is important that our results have such mathematical guarantees. Our approach achieves fast mixing in high dimensions whilst retaining the convergence guarantees of a traditional PDE solver, and without the burden of evaluating this solver for proposals that are likely to be rejected. Numerical results are given using real and simulated data.

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models is the expectation-maximization (EM) algorithm. For problems with high-dimensional latent variables and large datasets, EM scales poorly because it needs to invert as many large covariance matrices as the number of data points. We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversion. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.

It is highly predicted that the roads and parking areas will be extremely congested with vehicles to the point that searching for a novel solution will not be an optional choice for conserving the sustainability rate of the overall humanity's development growth. Such issue could be overcome by developing modified generations of the Urban Air Mobility (UAM) vehicles that essentially depend on the Vertical and/or Short Take-Off and Landing (V/STOL) feature to increase the efficiency of landing capabilities on limited-space parking areas. The complexity of integrating an efficient and safe V/STOL feature in such UAM vehicles is notably difficult comparing with the conventional and normal techniques for landing and take-off. The efficient V/STOL feature should be carried out by a complete and collaborative Cyber-Physical System (CPS) processing architecture, such as the CPS-5C architecture. In this paper, we only proposed two CPS-5C physical layers of a V/STOL Autonomous Landing Guidance Assistant System (ALGAS2) processing unit to increase the reliability of the vertical landing mechanism. The proposed V/STOL-ALGAS2 system depends on Fuzzy Logic System (FLS) as the advanced control unit. Furthermore, the proposed ALGAS2 system depends on four symmetric and segregated processing ALGAS2 cores that processing the data in a fully parallel and independent manner to enhance many essential security and safety factors for the futuristic UAM vehicles. The proposed ALGAS2 digital circuits architecture has been designed using MATLAB and VHDL. Also, it has been further analyzed for the implementation and validation tests using the Intel Altera OpenVINO FPGA board. The proposed ALGAS processing unit attained a maximum computational processing performance of about 21.22 Giga Operations per Seconds (GOPS).

With only observational data on two variables, and without other assumptions, it is not possible to infer which one causes the other. Much of the causal literature has focused on guaranteeing identifiability of causal direction in statistical models for datasets where strong assumptions hold, such as additive noise or restrictions on parameter count. These methods are then subsequently tested on realistic datasets, most of which violate their assumptions. Building on previous attempts, we show how to use causal assumptions within the Bayesian framework. This allows us to specify models with realistic assumptions, while also encoding independent causal mechanisms, leading to an asymmetry between the causal directions. Identifying causal direction then becomes a Bayesian model selection problem. We analyse why Bayesian model selection works for known identifiable cases and flexible model classes, while also providing correctness guarantees about its behaviour. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions showing the usefulness of our method.

Boosting is a commonly used technique to enhance the performance of a set of base models by combining them into a strong ensemble model. Though widely adopted, boosting is typically used in supervised learning where the data is labeled accurately. However, in weakly supervised learning, where most of the data is labeled through weak and noisy sources, it remains nontrivial to design effective boosting approaches. In this work, we show that the standard implementation of the convex combination of base learners can hardly work due to the presence of noisy labels. Instead, we propose $\textit{LocalBoost}$, a novel framework for weakly-supervised boosting. LocalBoost iteratively boosts the ensemble model from two dimensions, i.e., intra-source and inter-source. The intra-source boosting introduces locality to the base learners and enables each base learner to focus on a particular feature regime by training new base learners on granularity-varying error regions. For the inter-source boosting, we leverage a conditional function to indicate the weak source where the sample is more likely to appear. To account for the weak labels, we further design an estimate-then-modify approach to compute the model weights. Experiments on seven datasets show that our method significantly outperforms vanilla boosting methods and other weakly-supervised methods.

This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs (MM-DAGs), which are commonly observed in complex systems, e.g., traffic, manufacturing, and weather systems, whose variables are multi-modal with scalars, vectors, and functions. This paper takes the traffic congestion analysis as a concrete case, where a traffic intersection is usually regarded as a DAG. In a road network of multiple intersections, different intersections can only have some overlapping and distinct variables observed. For example, a signalized intersection has traffic light-related variables, whereas unsignalized ones do not. This encourages the multi-task design: with each DAG as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their consensus and consistency are maximized. To this end, we innovatively propose a multi-modal regression for linear causal relationship description of different variables. Then we develop a novel Causality Difference (CD) measure and its differentiable approximator. Compared with existing SOTA measures, CD can penalize the causal structural difference among DAGs with distinct nodes and can better consider the uncertainty of causal orders. We rigidly prove our design's topological interpretation and consistency properties. We conduct thorough simulations and one case study to show the effectiveness of our MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

While the neural ODE formulation of normalizing flows such as in FFJORD enables us to calculate the determinants of free form Jacobians in O(D) time, the flexibility of the transformation underlying neural ODEs has been shown to be suboptimal. In this paper, we present AFFJORD, a neural ODE-based normalizing flow which enhances the representation power of FFJORD by defining the neural ODE through special augmented transformation dynamics which preserve the topology of the space. Furthermore, we derive the Jacobian determinant of the general augmented form by generalizing the chain rule in the continuous sense into the cable rule, which expresses the forward sensitivity of ODEs with respect to their initial conditions. The cable rule gives an explicit expression for the Jacobian of a neural ODE transformation, and provides an elegant proof of the instantaneous change of variable. Our experimental results on density estimation in synthetic and high dimensional data, such as MNIST, CIFAR-10 and CelebA (32 32), show that AFFJORD outperforms the baseline FFJORD through the improved flexibility of the underlying vector field.

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an efficient Gibbs sampler. The Gibbs sampler attains similar performances as the state-of-the-art Monte Carlo Markov chain methods, such as the Hamiltonian Monte Carlo or the Metropolis adjusted Langevin algorithm, both on real and synthetic data. By framing our analysis in the teacher-student setting, we introduce a thermalization criterion that allows us to detect when an algorithm, when run on data with synthetic labels, fails to sample from the posterior. The criterion is based on the fact that in the teacher-student setting we can initialize an algorithm directly at equilibrium.