The Constant Question: How to Build Modern Affordably
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The first way is to utilize an advanced or innovative construction system that reduces labor, reduces construction time, or utilizes unique materials. This will either reduce your labor cost, construction period and financing cost, or material cost. Different approaches to PreFab attempt to tap into this, but so far the success is in making Modern Design available where it was not before, but the cost is still higher than status quo on-site construction. Economy of scale is required to make this kind of approach work.
The second way is to leverage construction means, methods, and materials already in practice in the home building industry, using modern designs conceived with this in mind. In this way you are not asking crafts people and construction workers to do anything out of their normal day to day operation, you are not using materials that they are not familiar with, existing material supply chains can be maintained, the construction industry's business model is not expected to be revolutionized. You ride the economy of scale that the entire home building industry provides.
Everything you build modern will fall to some degree into one of these two approaches. The closer you can get to either extreme, then the more affordably you will be able to build.
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Managing Costs
Think creative, be open to your architect and or builders suggestions and search the web for deals, they're out there.
non-traditional methods
I don't want to discourage anyone from pursuing design goals that are outside of the norm, but if you want to find a path to keeping costs lower, then go down that path only for the most important things.

How to Build Modern Affordably
How? Most importantly, you get very creative with design. You open up spaces when necessary, you utilize space intelligently, you create functionality in your design. You get creative with materials...using traditional materials in interesting ways or finding values on innovative materials through extensive and exhaustive internet searches.
Obviously, much of good design is in the details. Creativity in design allows you to use traditional building techniques (and sometimes materials) in interesting and innovative ways, while keeping your costs in line with traditional construction.
The other part of that equation is that you need to stay on top of the process. The guys doing the work will not necessarily understand the design aesthetic. If that is the case, you generally need to be there to guide them. You have to be able to effectively communicate what you want. If left to their own devices, the results can be troubling.
Lastly, you design for standardized measurements of materials and efficient use of materials to minimize waste. Cost effective, but also environmentally friendly. IE...keep lengths of walls divisible by four... minimizing plumbing runs by centralizing kitchens, baths, laundry... I could go on.
Certainly, affordable is a relative term. What's affordable in New York or San Francisco is pure insanity in Kansas City or Chicago. The point is this...based on the build costs in your area, can you build a modern home for the same (or lesser) cost than traditional construction? Frankly, the answer is yes...you can.
I'll gladly post some pictures if someone tells me how. I'm also happy to email them to anyone who is intersted. I can be reached at formmodern@yahoo.com
Scott Fletcher