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Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many methods fail in accurately generalizing in the entire time interval $[0, T]$, when the training data is available only in a training time interval $[0, T_0]$, with $T_0

Early detection and localization of pancreatic cancer can increase the 5-year survival rate for patients from 8.5% to 20%. Artificial intelligence (AI) can potentially assist radiologists in detecting pancreatic tumors at an early stage. Training AI models require a vast number of annotated examples, but the availability of CT scans obtaining early-stage tumors is constrained. This is because early-stage tumors may not cause any symptoms, which can delay detection, and the tumors are relatively small and may be almost invisible to human eyes on CT scans. To address this issue, we develop a tumor synthesis method that can synthesize enormous examples of small pancreatic tumors in the healthy pancreas without the need for manual annotation. Our experiments demonstrate that the overall detection rate of pancreatic tumors, measured by Sensitivity and Specificity, achieved by AI trained on synthetic tumors is comparable to that of real tumors. More importantly, our method shows a much higher detection rate for small tumors. We further investigate the per-voxel segmentation performance of pancreatic tumors if AI is trained on a combination of CT scans with synthetic tumors and CT scans with annotated large tumors at an advanced stage. Finally, we show that synthetic tumors improve AI generalizability in tumor detection and localization when processing CT scans from different hospitals. Overall, our proposed tumor synthesis method has immense potential to improve the early detection of pancreatic cancer, leading to better patient outcomes., Comment: Big Task Small Data, 1001-AI, MICCAI Workshop, 2023

A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many applications, we have limited access to the information of the whole system, which motivates non-intrusive model reduction. One bottleneck is capturing the dynamics of the solution without knowing the physics inside the "black-box" system. DMD is a powerful tool to mimic the dynamics of the system and give a reliable approximation of the solution in the time domain using only the dominant DMD modes. However, DMD cannot reproduce the parametric behavior of the dynamics. Our contribution focuses on extending DMD to parametric DMD by RBF interpolation. Specifically, a RBF network is first trained using snapshot matrices at limited parameter samples. The snapshot matrix at any new parameter sample can be quickly learned from the RBF network. DMD will use the newly generated snapshot matrix at the online stage to predict the time patterns of the dynamics corresponding to the new parameter sample. The proposed framework and algorithm are tested and validated by numerical examples including models with parametrized and time-varying inputs.

We demonstrate that AI models can accurately segment liver tumors without the need for manual annotation by using synthetic tumors in CT scans. Our synthetic tumors have two intriguing advantages: (I) realistic in shape and texture, which even medical professionals can confuse with real tumors; (II) effective for training AI models, which can perform liver tumor segmentation similarly to the model trained on real tumors -- this result is exciting because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to real tumors. This result also implies that manual efforts for annotating tumors voxel by voxel (which took years to create) can be significantly reduced in the future. Moreover, our synthetic tumors can automatically generate many examples of small (or even tiny) synthetic tumors and have the potential to improve the success rate of detecting small liver tumors, which is critical for detecting the early stages of cancer. In addition to enriching the training data, our synthesizing strategy also enables us to rigorously assess the AI robustness., Comment: CVPR 2023

We develop a novel strategy to generate synthetic tumors. Unlike existing works, the tumors generated by our strategy have two intriguing advantages: (1) realistic in shape and texture, which even medical professionals can confuse with real tumors; (2) effective for AI model training, which can perform liver tumor segmentation similarly to a model trained on real tumors - this result is unprecedented because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to the model trained on real tumors. This result also implies that manual efforts for developing per-voxel annotation of tumors (which took years to create) can be considerably reduced for training AI models in the future. Moreover, our synthetic tumors have the potential to improve the success rate of small tumor detection by automatically generating enormous examples of small (or tiny) synthetic tumors., Comment: NeurIPS Workshop on Medical Imaging Meets NeurIPS, 2022

The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) has established moir\'e quantum matter as a new platform to explore interaction-driven and topological quantum phenomena. Multitudes of phases have been realized in moir\'e systems, but surprisingly, robust superconductivity has been one of the least common of all, initially found in MATBG and only more recently also in magic-angle twisted trilayer graphene (MATTG). While MATBG and MATTG share some similar characteristics, they also exhibit substantial differences, such as in their response to external electric and magnetic fields. This raises the question of whether they are simply two separate unique systems, or whether they form part of a broader family of superconducting materials. Here, we report the experimental realization of magic-angle twisted 4-layer and 5-layer graphene (MAT4G and MAT5G, respectively), which turn out to be superconductors, hence establishing alternating-twist magic-angle multilayer graphene as a robust family of moir\'e superconductors. The members of this family have flat bands in their electronic structure as a common feature, suggesting their central role in the observed robust superconductivity. On the other hand, there are also important variations across the family, such as different symmetries for members with even and odd number of layers. However, our measurements in parallel magnetic fields, in particular the investigation of Pauli limit violation and spontaneous rotational symmetry breaking, reveal that the most pronounced distinction is between the N=2 and N>2-layer structures. Our results expand the emergent family of moir\'e superconductors, providing new insight with potential implications for the design of novel superconducting materials platforms., Comment: 15 pages, 4 figures

The boundary of tumors (hepatocellular carcinoma, or HCC) contains rich semantics: capsular invasion, visibility, smoothness, folding and protuberance, etc. Capsular invasion on tumor boundary has proven to be clinically correlated with the prognostic indicator, microvascular invasion (MVI). Investigating tumor boundary semantics has tremendous clinical values. In this paper, we propose the first and novel computational framework that disentangles the task into two components: spatial vertex localization and sequential semantic classification. (1) A HCC tumor segmentor is built for tumor mask boundary extraction, followed by polar transform representing the boundary with radius and angle. Vertex generator is used to produce fixed-length boundary vertices where vertex features are sampled on the corresponding spatial locations. (2) The sampled deep vertex features with positional embedding are mapped into a sequential space and decoded by a multilayer perceptron (MLP) for semantic classification. Extensive experiments on tumor capsule semantics demonstrate the effectiveness of our framework. Mining the correlation between the boundary semantics and MVI status proves the feasibility to integrate this boundary semantics as a valid HCC prognostic biomarker.

Materials realization of chiral topological superconductivity is a crucial condition for observing and manipulating Majorana fermions in condensed matter physics. Here we develop a tight-binding description of Pb$_3$Bi/Ge(111), identified recently as an appealing candidate system for realizing chiral $p$-wave topological superconductivity [Nat. Phys. 15, 796 (2019)]. We first show that our phenomenological model can capture the two main features of the electronic band structures obtained from first-principles calculations, namely, the giant Rashba splitting and type-II van Hove singularity. Next, when the $s$-wave superconducting property of the parent Pb system is explicitly considered, we find the alloyed system can be tuned into a chiral topological superconductor with Chern number $\mathcal{C} = -2$, resulting from the synergistic effect of a sufficiently strong Zeeman field and the inherently large Rashba spin-orbit coupling. The nontrivial topology with $\mathcal{C} = -2$ is further shown to be detectable as two chiral Majorana edge modes propagating along the same direction of the system with proper boundaries. We finally discuss the physically realistic conditions to establish the predicted topological superconductivity and observe the corresponding Majorana edge modes, including the influence of the superconducting gap, Land\'{e} $g$-factor, and critical magnetic field. The present study provides useful guides in searching for effective $p$-wave superconductivity and Majorana fermions in two-dimensional or related interfacial systems., Comment: 8 pages, 3 figures, 1table