Bin Dong(董彬) Long CV, Short CV
Professor
Beijing International Center for Mathematical
Research (BICMR),
Center for Machine Learning Research (CMLR)
Office: BICMR，77101; Phone:
+8610-62744091
Email: dongbin {at} math {dot} pku {dot} edu {dot} cn
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About -- Biography -- Events -- Publications -- Teaching
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Research Philosophy
My research philosophy has consistently been driven by the dual
aspiration of devising effective models and algorithms to address real-world
challenges while distilling novel mathematical problems during this process. In
essence, I aim to contribute to both practical applications and the advancement
of mathematics itself. This dualism has served as the cornerstone of my
research endeavors.
Areas of Focus
My primary research areas converge on biomedical imaging, particularly in
image reconstruction, image analysis, and auxiliary decision-making in clinical
diagnosis leveraging images and other medical data.
Earlier Career
During my doctoral and postdoctoral years, I have developed various
models and algorithms within the frameworks of Partial Differential Equations
(PDEs) and wavelets. These include designing PDE models for cerebral aneurysm
segmentation to facilitate subsequent geometric measurement (Ref);
integrating the notion of PDEs, level-set methods and wavelet transforms to
create computational tools for cardiovascular plaque quantification (Ref);
formulating CT image reconstruction models by exploiting the property of sparse
approximation of wavelet frame transforms (Ref1,
Ref2,
Ref3);
and optimizing radiation therapy for cancer mathematically (Ref)
which was later reported by phys.org.
Unveiling the
Connection: PDEs and Wavelets
Throughout the course of addressing these applied problems, I became
increasingly aware of the striking algorithmic resemblance between PDEs and wavelets.
This led to an investigative journey with collaborators to explore any
intrinsic relationships between these two paradigms, which had evolved
independently in the field of imaging for nearly three decades. We discovered
profound connections, unsettling traditional views and establishing an
asymptotic convergence relationship between wavelet-based optimization models
and PDE models. (Ref1,
Ref2,
Ref3,
Ref4)
This theoretical insight effectively bridged the geometric interpretations of
differential operators with the sparse approximations and multi-scale nature of
wavelets, inspiring new models that amalgamated the strengths of both PDEs and
wavelets. In particular, this insight has led to new wavelet frame-based image
segmentation models for medical images (Ref).
Notably, our collaborative paper on wavelet frame-based segmentation of
ultrasound videos (Ref)
with my colleagues at Shanghai Jiao Tong University and National University of
Singapore gained media attention, including coverage by SIAM
News, Science
Daily, etc.
Journey into
Machine Learning
My initial venture into machine learning commenced in 2014 resulting in a
sole-authored paper that introduced wavelet frames into semi-supervised
learning models on graphs and point clouds (Ref),
as well as a work on sparse linear discriminant analysis with my colleagues
from the statistics program at the University of Arizona (Ref).
However, it was not until 2015-2016 that I fully grasped the revolutionary
impact of deep learning, particularly on biomedical imaging problems. It was
also during this period that our earlier works on unveiling the connections
between PDEs and wavelets contributed to a unified perspective on these
mathematical models, which later informed our mathematical understanding of
deep neural networks.
Subsequently, I led my team to pivot our focus
towards deep learning methodologies. The core motive has been to explore the
algorithmic relations between traditional mathematical methods like PDEs and
wavelets and the data-driven models in deep learning. This exploration
culminated in two important works of mine between 2017 and 2018: the
establishment of the link between numerical differential equations and deep
neural network architectures, leading to the development of ODE-Net (Ref)
and PDE-Net (Ref1,
Ref2),
which were empirically validated on large-scale datasets. Through this and
several subsequent research studies, we gradually developed a novel generic
methodology for synergistically integrating mathematical modeling and machine
learning techniques. We have been constantly practicing and
refining this generic methodology in my research endeavors ever since (e.g.
examples in “Detour to Scientific Computing”).
The core focus of my presentation at the 2022 International Congress of
Mathematicians (ICM) was to elucidate the intricate connections between PDEs
and wavelets, as well as the links between discrete differential equations and
deep neural networks. These “bridges”
have intriguing implications for the fields of computational imaging and
scientific computing, which were thoroughly discussed in my talk and the
corresponding proceedings and notes (Ref1, Ref2).
Branching into Scientific Computing
Upon understanding deep neural networks through the lens of numerical
differential equations, it became natural to tackle challenges in scientific
computing, specifically, PDE-based forward and inverse problems. For the
forward problems, we blended numerical methods for conservation laws and
multigrid methods with deep reinforcement learning and meta-learning. (Ref1, Ref2) More recently, we discovered
a connection between meta-learning and reduced-order modeling, paving the way
for a new technique in approximating the solution manifold of parametric PDEs.
(Ref1, Ref2) For inverse problems, our
focus has been primarily on imaging, where we proposed several ways of melding
deep learning techniques with traditional mathematical algorithms (Ref1,
Ref2, Ref3, Ref4).
Clinical
Applications and Translational Research
Since 2019, I have embarked on an extensive collaboration with Peking
University Cancer Hospital, focusing on clinical auxiliary diagnostic issues.
This has resulted in a series of exciting progresses in medical image analysis,
contributing valuable tools for clinical practice that have seen successful
adoption and some degree of translational implementation.(Ref1, Ref2, Ref3, Ref4)
Future Research
Avenues
In my academic trajectory, I have encountered two major challenges that
will guide my research focus for the next n+1 years.
― AI for
Computational Imaging: Addressing the 'Boutique' Nature of Biomedical Imaging
Models:
The first challenge is rooted in the need for a unified and robust model
in the realm of biomedical imaging. Currently, while the fusion of machine
learning with first-principles modeling has proven powerful, its utility often
rests on designing specific models for specific scenarios—a
"boutique" approach that is neither efficient nor universally
applicable. In light of this, my future research aims to construct a
foundational model for computational imaging. This endeavor will focus on two
key tasks: firstly, to seamlessly integrate the three stages of computational
imaging, namely sensing, reconstruction, and analysis; and secondly, to
amalgamate various imaging modalities into a comprehensive framework. This
unified model aims to better address real-world challenges encountered in
biomedical imaging.
The quest for a foundational model in computational imaging is
intrinsically linked to the universal principles governing wave-matter
interactions, which underpin virtually all imaging modalities. These
interactions can be elegantly described through PDEs. Recognizing this, our
research endeavors to lay the groundwork for a foundational model that
encompasses the diverse spectrum of PDEs inherent in imaging processes (and
beyond). Our current trajectory has seen us making promising strides in the
one-dimensional domain (Ref), marking
the initial phase of a comprehensive journey towards achieving a holistic model
for computational imaging.
― AI for
Mathematics: Building AI Copilot for Theoretical Research
The second challenge stems from the observation that advances in
artificial intelligence technology have outpaced the development of underlying
theory. Traditional theoretical research has been effective in guiding the
design of algorithms, but it is increasingly lagging in the realm of AI. One
key bottleneck is the inefficiency of theory-driven research, where researchers
often find it difficult to flexibly apply a breadth of mathematical knowledge
or to innovatively create new mathematical concepts and tools. To address this,
my future work plans to develop an AI assistant designed to facilitate
mathematical theory research. This assistant would serve dual functions: to
inspire mathematical thinking and to automate several aspects of theoretical
work. This includes, but is not limited to, the verification of theorem proofs,
automated theorem proving, and semantic search of mathematical concepts and
results. While we've made some initial (but exciting) steps in this direction
in collaboration with colleagues from Hong Kong University, specifically in the
application of machine learning tools to explore affine Deligne-Lusztig
varieties (Ref), there is still
much to be done to fully realize the potential of AI as a tool for advancing
mathematical theory.
By focusing on these two pivotal challenges, I aim
to modestly contribute to both the realm of biomedical imaging and the
advancement of mathematics itself.
Last updated: 02/2024.