Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are widely-used. However, traditional numerical algorithms are computationally expensive and challenging in handling multiphysics systems. Recently, using neural networks to solve PDEs has made significant progress, called physics-informed neural networks (PINNs). PINNs encode physical laws into neural networks and learn the continuous solutions of PDEs. For the training of PINNs, existing methods suffer from the problems of inefficiency and unstable convergence, since the PDE residuals require calculating automatic differentiation. In this paper, we propose Dynamic Mesh-based Importance Sampling (DMIS) to tackle these problems. DMIS is a novel sampling scheme based on importance sampling, which constructs a dynamic triangular mesh to estimate sample weights efficiently. DMIS has broad applicability and can be easily integrated into existing methods. The evaluation of DMIS on three widely-used benchmarks shows that DMIS improves the convergence speed and accuracy in the meantime. Especially in solving the highly nonlinear Schr\"odinger Equation, compared with state-of-the-art methods, DMIS shows up to 46% smaller root mean square error and five times faster convergence speed. Code are available at //github.com/MatrixBrain/DMIS.
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Despite the promising future of autonomous robots, several key issues currently remain that can lead to compromised performance and safety. One such issue is latency, where we find that even the latest embedded platforms from NVIDIA fail to execute intelligence tasks (e.g., object detection) of autonomous vehicles in a real-time fashion. One remedy to this problem is the promising paradigm of edge computing. Through collaboration with our industry partner, we identify key prohibitive limitations of the current edge mindset: (1) servers are not distributed enough and thus, are not close enough to vehicles, (2) current proposed edge solutions do not provide substantially better performance and extra information specific to autonomous vehicles to warrant their cost to the user, and (3) the state-of-the-art solutions are not compatible with popular frameworks used in autonomous systems, particularly the Robot Operating System (ROS). To remedy these issues, we provide Genie, an encapsulation technique that can enable transparent caching in ROS in a non-intrusive way (i.e., without modifying the source code), can build the cache in a distributed manner (in contrast to traditional central caching methods), and can construct a collective three-dimensional object map to provide substantially better latency (even on low-power edge servers) and higher quality data to all vehicles in a certain locality. We fully implement our design on state-of-the-art industry-adopted embedded and edge platforms, using the prominent autonomous driving software Autoware, and find that Genie can enhance the latency of Autoware Vision Detector by 82% on average, enable object reusability 31% of the time on average and as much as 67% for the incoming requests, and boost the confidence in its object map considerably over time.
We propose a new RowHammer mitigation mechanism, CoMeT, that prevents RowHammer bitflips with low area, performance, and energy costs in DRAM-based systems at very low RowHammer thresholds. The key idea of CoMeT is to use low-cost and scalable hash-based counters to track DRAM row activations. CoMeT uses the Count-Min Sketch technique that maps each DRAM row to a group of counters, as uniquely as possible, using multiple hash functions. When a DRAM row is activated, CoMeT increments the counters mapped to that DRAM row. Because the mapping from DRAM rows to counters is not completely unique, activating one row can increment one or more counters mapped to another row. Thus, CoMeT may overestimate, but never underestimates, a DRAM row's activation count. This property of CoMeT allows it to securely prevent RowHammer bitflips while properly configuring its hash functions reduces overestimations. As a result, CoMeT 1) implements substantially fewer counters than the number of DRAM rows in a DRAM bank and 2) does not significantly overestimate a DRAM row's activation count. Our comprehensive evaluations show that CoMeT prevents RowHammer bitflips with an average performance overhead of only 4.01% across 61 benign single-core workloads for a very low RowHammer threshold of 125, normalized to a system with no RowHammer mitigation. CoMeT achieves a good trade-off between performance, energy, and area overheads. Compared to the best-performing state-of-the-art mitigation, CoMeT requires 74.2x less area overhead at the RowHammer threshold 125 and incurs a small performance overhead on average for all RowHammer thresholds. Compared to the best-performing low-area-cost mechanism, at a very low RowHammer threshold of 125, CoMeT improves performance by up to 39.1% while incurring a similar area overhead. CoMeT is openly and freely available at //github.com/CMU-SAFARI/CoMeT.
In the rapidly evolving landscape of deep learning, the quest for models that balance expressivity with computational efficiency has never been more critical. This paper introduces Orchid, a novel architecture that reimagines sequence modeling by incorporating a new data-dependent convolution mechanism. Orchid is designed to address the inherent limitations of traditional attention mechanisms, particularly their quadratic complexity, without compromising the ability to capture long-range dependencies and in-context learning. At the core of Orchid lies the data-dependent convolution layer, which dynamically adjusts its kernel conditioned on input data using a dedicated conditioning neural network. We design two simple conditioning networks that maintain shift equivariance in the adaptive convolution operation. The dynamic nature of data-dependent convolution kernel, coupled with gating operations, grants Orchid high expressivity while maintaining efficiency and quasilinear scalability for long sequences. We rigorously evaluate Orchid across multiple domains, including language modeling and image classification, to showcase its performance and generality. Our experiments demonstrate that Orchid architecture not only outperforms traditional attention-based architectures such as BERT and Vision Transformers with smaller model sizes, but also extends the feasible sequence length beyond the limitations of the dense attention layers. This achievement represents a significant step towards more efficient and scalable deep learning models for sequence modeling.
Simulation-based inference (SBI) is constantly in search of more expressive algorithms for accurately inferring the parameters of complex models from noisy data. We present consistency models for neural posterior estimation (CMPE), a new free-form conditional sampler for scalable, fast, and amortized SBI with generative neural networks. CMPE combines the advantages of normalizing flows and flow matching methods into a single generative architecture: It essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be tailored to the structure of the estimation problem. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on three hard low-dimensional problems but also achieves competitive performance in a high-dimensional Bayesian denoising experiment and in estimating a computationally demanding multi-scale model of tumor spheroid growth.
Uncertainty quantification (UQ) to detect samples with large expected errors (outliers) is applied to reactive molecular potential energy surfaces (PESs). Three methods - Ensembles, Deep Evidential Regression (DER), and Gaussian Mixture Models (GMM) - were applied to the H-transfer reaction between ${\it syn-}$Criegee and vinyl hydroxyperoxide. The results indicate that ensemble models provide the best results for detecting outliers, followed by GMM. For example, from a pool of 1000 structures with the largest uncertainty, the detection quality for outliers is $\sim 90$ \% and $\sim 50$ \%, respectively, if 25 or 1000 structures with large errors are sought. On the contrary, the limitations of the statistical assumptions of DER greatly impacted its prediction capabilities. Finally, a structure-based indicator was found to be correlated with large average error, which may help to rapidly classify new structures into those that provide an advantage for refining the neural network.
In the field of class incremental learning (CIL), genera- tive replay has become increasingly prominent as a method to mitigate the catastrophic forgetting, alongside the con- tinuous improvements in generative models. However, its application in class incremental object detection (CIOD) has been significantly limited, primarily due to the com- plexities of scenes involving multiple labels. In this paper, we propose a novel approach called stable diffusion deep generative replay (SDDGR) for CIOD. Our method utilizes a diffusion-based generative model with pre-trained text- to-diffusion networks to generate realistic and diverse syn- thetic images. SDDGR incorporates an iterative refinement strategy to produce high-quality images encompassing old classes. Additionally, we adopt an L2 knowledge distilla- tion technique to improve the retention of prior knowledge in synthetic images. Furthermore, our approach includes pseudo-labeling for old objects within new task images, pre- venting misclassification as background elements. Exten- sive experiments on the COCO 2017 dataset demonstrate that SDDGR significantly outperforms existing algorithms, achieving a new state-of-the-art in various CIOD scenarios. The source code will be made available to the public.
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem. In addition, we discuss generalizability and computational cost of the learned mesh motion operators.
We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the ensuing system of fractional linear equations is solved resorting to a Monte Carlo evaluation of the corresponding Mittag-Leffler matrix function. This is accomplished through the approximation of the expected value of a suitable multiplicative functional of a stochastic process, which consists of a Markov chain whose sojourn times in every state are Mittag-Leffler distributed. The resulting algorithm is able to calculate the solution at conveniently chosen points in the domain with high efficiency. In addition, we present how to generalize this algorithm in order to compute the complete solution. For several large-scale numerical problems, our method showed remarkable performance in both shared-memory and distributed-memory systems, achieving nearly perfect scalability up to 16,384 CPU cores.
Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.
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